The citizens of London, who act as a Greek chorus throughout the play, drop a body bag and pour ashes into a shallow grave. Sweeney Todd rises forth ("The Ballad of Sweeney Todd"), and introduces the drama.

Act I
In 1846, young sailor Anthony Hope and the mysterious Sweeney Todd, whom Anthony has recently rescued at sea and befriended, dock in London. A beggar woman sexually solicits them, appearing to recognize Todd for a moment ("No Place Like London"), and Todd shoos her away. Todd obliquely relates some of his troubled past to Anthony: he was a naïve barber, "removed...from his plate" by a corrupt judge who lusted after Todd's wife ("The Barber and His Wife"). Leaving Anthony, Todd enters a meat pie shop on Fleet Street, where the owner, the slatternly widow Mrs. Lovett, laments the scarcity of meat and customers ("Worst Pies in London"). When Todd asks after the empty upstairs apartment, she reveals that its former tenant, Benjamin Barker, was transported for life based on false charges by Judge Turpin, who, along with his servant, Beadle Bamford, then lured Barker's wife Lucy to a masked ball at the Judge's home and raped her ("Poor Thing").

Todd's reaction reveals that he is himself Benjamin Barker. Promising to keep his secret, Mrs. Lovett explains that Lucy poisoned herself with arsenic and that their then-infant daughter, Johanna, became the Judge's ward. Todd swears revenge on the Judge and the Beadle, and Mrs. Lovett presents Todd with his old collection of sterling silver straight razors, which persuades Todd to take up his old profession ("My Friends" and "The Ballad of Sweeney Todd" – reprise). Elsewhere, Anthony spies a beautiful girl singing at her window ("Green Finch and Linnet Bird"), and the beggar woman tells him that her name is Johanna. Unaware that Johanna is his friend Todd's daughter, Anthony is immediately enamored ("Ah, Miss"), and he pledges to return for her, even after the judge and the Beadle threaten him and chase him away ("Johanna").

In the crowded London marketplace, flamboyant Italian barber Adolfo Pirelli and his simple-minded young assistant Tobias Ragg pitch a dramatic cure-all for hair loss ("Pirelli's Miracle Elixir"). Todd and Lovett soon arrive; as part of his plan to establish his new identity, Todd exposes the elixir as a sham, challenges Pirelli to a shaving competition and easily wins ("The Contest"), inviting the impressed Beadle for a free shave ("The Ballad of Sweeney Todd" – reprise 2). Several days later, Judge Turpin flagellates himself in a frenzy over a growing lust for Johanna, but instead resolves to marry her himself ("Johanna – Mea Culpa").

Todd awaits the Beadle's arrival with mounting impatience, but Mrs. Lovett tries to soothe him ("Wait"). When Anthony tells Todd of his plan to ask Johanna to elope with him, Todd, eager to reunite with his daughter, agrees to let them use his barbershop as a safehouse. As Anthony leaves, Pirelli and Tobias enter, and Mrs. Lovett takes Toby downstairs for a pie. Alone with Todd, Pirelli drops his Italian accent and reveals that he is really Daniel O'Higgins, Benjamin Barker's former assistant. He knows Todd's true identity (having recognized Barker's illustrious shaving tools during their earlier competition) and demands half his income for life. (In the film, the name is not Daniel O'Higgins but "Davy Collins".) Todd kills O'Higgins by slitting his throat ("Pirelli's Death" and "The Ballad of Sweeney Todd" – reprise 3) and temporarily hides his body. Meanwhile, Johanna and Anthony plan their elopement ("Kiss Me"), while the Beadle recommends Todd's grooming services to the Judge so that the judge may better win Johanna's affections ("Ladies in Their Sensitivities").

Panicked at first on learning of Pirelli's murder, Mrs. Lovett swipes his leftover coin purse and then asks Todd how he plans to dispose of the body. Suddenly, the judge enters; Todd quickly seats him and lulls him with a relaxing conversation ("Pretty Women"). Before Todd can kill the judge, however, Anthony re-enters and blurts out his elopement plan. The angry judge storms out, vowing never to return and to send Johanna away. Todd drives Anthony out in a fit of fury and, reminded of the evil he sees in London, resolves to depopulate the city by murdering his future customers since all people deserve to die: the rich to be punished for their corruption, and the poor to be relieved of their misery ("Epiphany"). While discussing how to dispose of Pirelli's body, Mrs. Lovett is struck by a sudden idea and suggests that they use the bodies of Todd's victims in her meat pies, and Todd happily agrees ("A Little Priest").

Act II
Several weeks later, Mrs. Lovett's pie shop has become a successful business, and Toby works there as a waiter. The food is very popular ("God, That's Good!"). Todd has acquired a special mechanical barber's chair that allows him to kill clients and then send their bodies directly through a chute into the pie shop's basement bakehouse. Casually slitting his customers' necks, Todd despairs of ever seeing Johanna, while Anthony searches London for her ("Johanna – Quartet"). Anthony finds Johanna locked away in a private lunatic asylum, but barely escapes being placed under arrest by the Beadle. After a day of hard work, while Todd remains fixated on his revenge, Mrs. Lovett envisions a seaside retirement ("By the Sea"). Anthony arrives to beg Todd for help to free Johanna, and Todd, revitalized, instructs Anthony to rescue her by posing as a wigmaker intent on purchasing inmates' hair ("Wigmaker Sequence" and "The Ballad..." – reprise 4). However, once Anthony has departed, Todd sends a letter informing the Judge that Anthony will bring Johanna to his shop just after dark, and that he will hand her over ("The Letter") in order to lure him back to the shop .

In the pie shop, Toby tells Mrs. Lovett of his skepticism about Todd and his own desire to protect her ("Not While I'm Around"). When he recognizes Pirelli's coin purse in Mrs. Lovett's hands, she distracts him by showing him the bakehouse, instructing him how to work the meat grinder and the oven before locking him in. Upstairs, she encounters the Beadle at her harmonium; he has been asked by Lovett's neighbors to investigate the strange smoke and stench from the pie shop's chimney. Mrs. Lovett stalls the Beadle with "Parlor Songs" until Todd returns to offer the Beadle his promised "free shave"; Mrs. Lovett loudly plays her harmonium to cover the Beadle's screams above as Todd dispatches him. In the basement, Toby discovers hair and fingernails in a pie he has been eating, just as the Beadle's fresh corpse comes tumbling through the chute. Terrified, he flees into the sewers below the bakehouse. Mrs. Lovett then informs Todd that Toby has found out about their secret and they plot to kill him.

Anthony arrives at the asylum to rescue Johanna, but is exposed when Johanna recognizes him. Anthony draws a pistol given to him by Todd, but cannot bring himself to shoot Jonas Fogg, the corrupt asylum owner; Johanna grabs the pistol and kills Fogg. As Anthony and Johanna flee, the asylum's freed inmates prophesy the end of the world, while Todd and Mrs. Lovett hunt through the sewers for Toby, and the beggar woman fears what has become of the Beadle ("City on Fire/Searching").

Anthony and Johanna (now disguised as a sailor) arrive at Todd's empty shop. Anthony leaves to seek a coach after he and Johanna reaffirm their love ("Ah Miss" – reprise). Johanna hears the beggar woman entering and hides in a trunk in the barbershop. The beggar woman seems to recognize the room. Todd enters and tries to force her to leave as she again seems to recognize him ("Beggar Woman's Lullaby"). Hearing the Judge outside, a frantic Todd kills the beggar woman, sending her body down the chute barely a moment before the Judge bursts in. Todd assures the Judge that Johanna is repentant, and the judge asks for a quick splash of cologne.

Once he has the Judge in his chair, Todd soothes him with another conversation on women, but this time he alludes to their "fellow tastes, in women at least". The Judge recognizes him as "Benjamin Barker!" just before Todd slashes his throat and sends him hurtling down the chute ("The Judge's Return"). Remembering Toby, Todd starts to leave, but, realizing he has left his razor behind, returns just as the disguised Johanna rises, horrified, from the trunk. Not recognizing her, Todd attempts to kill her, just as Mrs. Lovett shrieks from the bakehouse below, providing a distraction for Johanna to escape. Downstairs, Mrs. Lovett is struggling with the dying Judge, who claws at her. She then attempts to drag the beggar woman's body into the oven, but Todd arrives and, through a shaft of light, sees the lifeless face clearly for the first time: the beggar woman was his wife Lucy. Horrified, Todd accuses Mrs. Lovett of lying to him. Mrs. Lovett frantically denies it, explaining that Lucy did indeed poison herself, but lived, although the attempt left her insane. Mrs. Lovett then tells Todd she loves him and would be a better wife than Lucy ever could have been. Todd feigns forgiveness, dancing manically with Mrs. Lovett until he hurls her into the oven, burning her alive. Full of despair and in shock, Todd embraces the dead Lucy. Toby, now quite insane and his hair turned white, crawls up from the sewer babbling nursery rhymes to himself. He picks up Todd's fallen razor and slits Todd's throat. As Todd falls dead and Toby drops the razor, Anthony, Johanna and some others break into the bakehouse. Toby, heedless of them, begins turning the meat grinder, crooning Mrs. Lovett's previous instructions to him ("Final Scene").

Epilogue
The ensemble cast, soon joined by the risen Todd and Mrs. Lovett, sing a final reprise of "The Ballad of Sweeney Todd" warning against revenge (though admitting that "everyone does it"). Tearing off their costumes, the company exits. Todd sneers at the audience for a moment and vanishes.