There’s something delightfully over-the-top about Teeth, a new pop-rock musical inspired by the 2007 cult horror comedy of the same name centering on an uptight teenager who discovers she has a lethal set of vaginal chompers ready to snap at any unwanted male intrusion. Bloody severed penises held aloft and played for laughs? This is definitely not the stuff of traditional musical theater. (The show just opened at Off Broadway’s Playwrights Horizons.)

For a while, director Sarah Benson’s winning cast treads that tricky tightrope required to deliver a biting (literally) satire of hot-button issues like evangelical Christianity, contemporary sexuality, and gender roles. Alyse Alan Louis delivers the right mix of innocence and lust as our sharp-toothed heroine, Dawn, the It girl in her uber-Christian circle who flaunts her Promise ring while barely suppressing her lust for her re-virgined jock boyfriend, Tobey (Jason Gotay). Dawn’s strident religiosity and sex negativity is supported by her stepdad pastor (played with televangelistic malevolence by Steven Pasquale) while alienating her budding incel of a stepbrother (Will Connolly), who seeks out the support of an online group railing against a “feminocracy” that seeks to subvert traditional masculinity. (“The weaker sex has weakened us,” they sing.)

The book, by Anna K. Jacobs and Michael R. Jackson (A Strange Loop), goes well beyond the original movie, layering in more satire, Grand Guignol flourishes, and classic teenage horror/comedy tropes borrowed from Carrie, Saved, and Heathers — other cult movies that have all gotten the stage musical treatment. Jacobs has a flare for writing infectious pop-rock, which gets a wonderful spiky lift from Jackson’s witty and sometimes deliberately crass lyrics. Consider the transition from the bubblegum-pop of Dawn and Tobey’s pro-virginity duet, “Modest Is Hottest” (“You don’t tempt fate with spaghetti straps / you’re a girl who keeps it all under wraps”), to Dawn’s altogether raunchier confession of her physical desires (“My panties are wet / but it’s not blood or sweat”) in a club-ready girl group tune backed up a chorus of her fellow Promise ring-wearing teens.

The solidly sung score become more stridently bombastic, and less musically interesting, as the show progresses — and the story too becomes less coherent. Tobey is introduced as a sweet hunk, genuinely attracted to Dawn and even more in control of his impulses than she is, but then he suddenly morphs into a skinnydipping date rapist who gets a rather disproportionate punishment: not merely castration, but death. The other men in Dawn’s life meet similar fates, including (improbably) her closeted gay bestie (Jared Loftin, making the most of a head-scratcher of a character). There’s a sense that the show is following an agenda rather than a well-thought-out narrative structure — though at least one of Dawn’s victims, a skeevy gynecologist played by Pasquale in a gray-haired wig, gets a hilarious, toe-tapping soft-shoe number about the joys of “spelunking in the birth canal.”

Teeth works best when Jacobs and Jackson stay true to their core story, focusing on flawed characters trying their best in often larger-than-life circumstances. But midway through, the focus shifts from a satirical story to a mythic one — making the subtext of the narrative a more literal life-and-death battle between capital-F Forces. Benson’s production design also goes hyperbolic, with stage effects (by Jeremy Chernick) on Adam Rigg’s church-hall-inspired set that bring the hellfire to the finale in a literal way. It’s as if this affair to dismember has bitten off more than it can chew.