The company assembles as a chorus of London's citizens to perform a no-frills burial, dumping a body bag into a shallow grave. As they sing, Sweeney Todd rises from the grave as though summoned forth ("The Ballad of Sweeney Todd: Attend the Tale of Sweeney Todd"), before the actual play begins, set some months before the burial. The company continues to appear throughout the show to comment on the action of the play through song.
The year is 1846. A young sailor named Anthony Hope rides a ship into London, full of joy about his return home; conversely, the aloof Sweeney Todd, whom Anthony recently rescued during a storm at sea, is grim and uneasy. On land, Todd's mood is worsened by a half-mad Beggar Woman who sexually solicits both Anthony and Todd, and appears to recognize Todd ("No Place Like London"). Before the two shipmates part, Todd discourages Anthony's innocently happy worldview by recounting the tragic story of a young and naïve barber, his beautiful wife, and the lustful judge who exiled him to pursue her ("The Barber and His Wife"). Todd soon enters a meat pie shop on Fleet Street, where he encounters the shop's proprietress, Mrs. Nellie Lovett, who laments about the difficult economic times ("Worst Pies in London"). When Todd asks about her unoccupied upstairs apartment, she recounts the sad tale of the previous tenant, a barber named Benjamin Barker. Barker was sentenced on false charges by the corrupt Judge Turpin because of the Judge's lust for Barker's wife, Lucy. Mrs. Lovett reveals how, once Barker had been transported to Botany Bay in Australia, the Judge and his cohort, Beadle Bamford, then lured Lucy to the Judge's home and raped her ("Poor Thing"). Upon hearing the tale, Todd's reaction of explosive despair confirms Mrs. Lovett's suspicions that he is himself Benjamin Barker, back from Australia. She tells Todd that his wife poisoned herself and his then-infant daughter, Johanna, became a ward of the Judge. Todd swears revenge on the Judge and Beadle before Mrs. Lovett reveals Todd's old collection of sterling silver straight razors, which she has kept hidden for years, telling him that he can now live above her shop and become a barber again ("My Friends" and "The Ballad of Sweeney Todd: Lift Your Razor High, Sweeney!").
Meanwhile, Anthony, walking through Kearny's Lane, notices an exquisite blonde girl singing at a window ("Green Finch and Linnet Bird"). The Beggar Woman again passes by and tells Anthony that the girl is Johanna, Judge Turpin's ward. Unaware that Johanna is his friend Todd's daughter, Anthony is immediately smitten ("Ah, Miss") and pledges to woo her; however, the Judge and the Beadle threaten Anthony off by violently killing a bird that he buys for Johanna. Anthony swears to rescue her from such vile captors ("Johanna"). Meanwhile, in the crowded marketplace, renowned "Italian" barber Adolfo Pirelli and his simple-minded assistant, Tobias Ragg, pitch a cure-all for hair loss ("Pirelli's Miracle Elixir"). Todd, after exposing the elixir as a hoax, challenges Pirelli to a shaving competition. Pirelli puts on a grandiose show before Beadle Bamford and other townsfolk, but Todd wins easily ("The Contest"). Todd invites the impressed Beadle to visit his parlor some time for a complimentary shave ("The Ballad of Sweeney Todd: Sweeney Pondered and Sweeney Planned").
Several days later, as Todd waits for the Beadle's arrival, Mrs. Lovett urges the persistence of his diminishing patience ("Wait"), when Anthony enters the shop. He tells Todd of his sudden romance with Johanna and requests to use Todd's barbershop as a safe house for the girl. No sooner has Anthony left than Pirelli and Tobias visit the shop; Mrs. Lovett distracts Toby downstairs, leaving Todd alone with Pirelli, who drops his Italian accent to reveal an Irish one. Pirelli declares his true identity as Danny O'Higgins and recounts having served as an assistant to Todd fifteen years ago. O'Higgins now attempts to blackmail his former employer; however, Todd suddenly strangles O'Higgins and dumps his body into an empty trunk. Once Toby—seeking his master—has again entered and exited, Todd opens the trunk and finishes off O'Higgins by slitting his throat ("The Ballad of Sweeney Todd: His Hands Were Quick, His Fingers Strong").
Across town, Judge Turpin is tormented by his lust for Johanna, finally announcing his intention to marry her ("Johanna–Mea Culpa"). Disgusted by the prospect, Johanna and Anthony plan to elope ("Kiss Me"). At the same time, the Beadle recommends Todd's services to the Judge, in order to improve his appearance for better winning Johanna's affections ("Ladies in Their Sensitivities"). Mrs. Lovett continues to distract Toby until the Judge enters Todd's shop. Although caught off guard and eager for blood, Todd prepares to exact his revenge by first carefully calming the Judge ("Pretty Women"). Before Todd strikes, however, Anthony barges in to tell Todd about his and Johanna's plans, accidentally informing the enraged Judge, who storms out, vowing never to return. Todd, having lost his opportunity for vengeance, drives Anthony away before descending into furious madness and broadening his anger's target to all of humanity: by punishing the rich and corrupt, and relieving the poor of their misery, through death ("Epiphany"). Mrs. Lovett, however, is more practical while discussing how to dispose of O'Higgins' body and has a sudden burst of inspiration, suggesting through wordplay that they use the flesh of Todd's victims in her meat pies, an idea which Todd enthusiastically adopts ("A Little Priest").
Mrs. Lovett's pie shop has become a thriving business with even Toby helping to wait on its many customers ("God, That's Good!"). The only downside is the Beggar Woman, who continually hangs around the pie shop defaming Mrs. Lovett. Todd and Mrs. Lovett now have a specially-designed mechanical barber's chair that allows Todd to kill someone in the barbershop and then send the body through a chute directly into the pie shop's basement bakehouse for Mrs. Lovett to cook. Todd accustoms himself to the idea that he may never see Johanna again, spending his time methodically slashing throats, while Anthony longs to be with her romantically ("Johanna–Quartet"). After a day of hard work, Mrs. Lovett daydreams of a future life of retirement with Todd, though he appears uninterested ("By The Sea").
In the meantime, Anthony discovers that the Judge has committed Johanna to Fogg's Lunatic Asylum and, with Todd's help, plans to rescue her by infiltrating the asylum posing as a wigmaker intent on purchasing inmates' hair ("Wigmaker Sequence" and "The Ballad of Sweeney Todd: Sweeney'd Waited Too Long Before"). Jubilant at the possibility of having his revenge fulfilled after all, Todd sends a secret letter to notify the Judge about Anthony's plot, hoping to lure the Judge to his shop, where he writes that Anthony plans to return with Johanna. (The contents of the letter are sung aloud by a quintet from the company; "The Letter.")
In the pie shop, Toby expresses suspicions about Todd and his desire to protect Mrs. Lovett, whom he has come to view as a mother figure ("Not While I'm Around"). When he recognizes Pirelli's coin purse in Mrs. Lovett's possession, she refocuses his attention on learning how to work her meat grinder and other bakehouse machinery, secretly locking him alone in the basement when she leaves. Back upstairs, she encounters Beadle Bamford sitting at her harmonium, commissioned by neighbors to investigate the strange smoke and smells from the pie shop's chimney. Mrs. Lovett stalls for time before Todd arrives and offers the Beadle his promised "free shave"; Mrs. Lovett loudly plays music on her harmonium to cover the screams of the Beadle's demise above ("Parlor Songs"). Immediately after, Toby discovers a hair and fingernail in pie he samples when suddenly the Beadle's fresh corpse tumbles into the basement. Above, Mrs. Lovett informs Todd that Toby has figured them out and they head downstairs to dispose of him.
Anthony arrives at the asylum to rescue Johanna, but Fogg, the deranged owner of the asylum, attempts to stop them. Anthony brandishes a pistol but when he is unable to kill Fogg, Johanna instinctively grabs the weapon, aims true, and fires, fleeing with Anthony to Todd's parlor (Johanna disguised in sailor's clothing). The asylum's inmates pour out onto the streets, ecstatically proclaiming the end of the world; at the same time, Todd and Mrs. Lovett hunt for Toby in vain ("City on Fire/Searching"), abandoning their search when the Judge approaches. Alone in Todd's parlor while Anthony seeks out a coach on the street, Johanna quickly hides as the Beggar Woman, especially frenzied, enters the barbershop. Todd stumbles upon the Beggar Woman and, anticipating the Judge's arrival, frantically slits her throat, sending her down the chute a moment before the Judge bursts in. Todd assures the Judge that Johanna is totally repentant and the Judge lustfully asks for a quick face massage and some cologne before reuniting with her. Once he has the Judge in his chair, Todd soothes then suddenly mocks him, alerting the Judge to his former identity. Both the Judge and Todd scream "Benjamin Barker!" before Todd, at last, passionately slashes his enemy's throat and sends him hurtling down the chute ("The Judge's Return"). Johanna, who has heard every noise, emerges from her hiding place in the room and is also nearly slain by Todd; however, Mrs. Lovett shrieks from the bakehouse below, providing a distraction for Johanna to escape out the door.
Down in the bakehouse, Mrs. Lovett panics while struggling with the wounded Judge, who claws at her before finally dying. Storming into the room and seeing the face of the Beggar Woman clearly with the oven's light, Todd realizes in horror that she is in fact his wife Lucy. When Mrs. Lovett said that Lucy had poisoned herself, Todd interpreted this to mean his wife was dead. Todd now furiously accuses Mrs. Lovett of deceiving him, but Mrs. Lovett maintains her guiltlessness, saying that although Lucy had indeed taken poison, she did not die but instead went insane. Lovett says she withheld the whole truth from Todd in order to spare his feelings because she loves him. Todd feigns calm forgiveness, waltzing Lovett over to the huge oven, abruptly hurling her into the fire, and slamming the doors shut. Todd then sinks to the floor and cradles his deceased wife in his arms. Toby, driven completely insane and with his hair now white from shock, reappears from the shadows, picks up Todd's fallen razor, and strikes at Todd's throat. As Anthony, Johanna, and some constables break into the bakehouse, Todd falls dead and Toby drops the razor, heedless of the others, while beginning to absentmindedly parody the motions of turning a meat grinder ("Final Scene").
The company assembles one last time to sing "The Ballad of Sweeney Todd." As the resurrected ghosts of Todd and Mrs. Lovett rise from their graves, they conclude that the capability for revenge is within all of us. The company exits with Todd and Mrs. Lovett being the last. Todd pauses at the large iron door at the back of the stage to look at Mrs. Lovett one final time before slamming the door in the audience's face.