So here’s the situation. You’ve got a dead cat on your hands, and when the owner finds out, he’s going to be really ticked off. What to do? Well, first call him (he’s out of town) and say the cat’s under the weather – that might cushion the blow for later. Meanwhile, find a neighborhood cat and try to pass it off as his. But wait, what if the dead cat’s black and this one’s orange? Hmmn … try covering it with shoe polish. Just make sure you don’t dip into that booze too much, or you may not finish the job before said owner returns. Whoops!

The setup of Martin McDonagh’s over stimulating if somewhat shallow “Lieutenant of Inishmore” could hardly be more sitcom-ready and innocuous – until you meet the cat owner in the second scene. Padraic (the chillingly efficient David Wilmot) has a torture victim strung up by his feet in a Northern Ireland warehouse and has already pried two toenails off (although he feels he’s been generous by confining the damage to one foot, making it easier for the fellow to walk to the hospital if and when he’s freed). Next up for his straight razor: one or both of the man’s nipples, which he may then feed to the guy.

Padraic’s sadistic tendencies have pushed him first into an extremist splinter faction of the IRA, and now into an even more extremist splinter faction of that group. He has one friend in the world, one thing he loves. Its name is Wee Thomas. Er, was Wee Thomas. Better hope that shoe polish works.

By juxtaposing this goofy premise with “Mad Padraic’s” mounting rage, Mr. McDonagh and director Wilson Milam (whose previous experiments in gore include the unforgettable “Killer Joe”) generate a steadily growing unease that culminates in a virtual abbatoir. All the while, Mr. McDonagh provides his usual trick endings, tartly profane dialogue, and blasts of familial violence: “Many’s the time I trampled on my mam when she was alive. After she’d died I stopped. There seemed no sense.”

This is the ghoulish/glib world of Quentin Tarantino, where only an occasional flash of ultraviolence interrupts the clever banter. But just as Mr. Tarantino vacillates between the clever but emotionally honest layers of works like “Jackie Brown” and “Pulp Fiction” and the grind-house giddiness of “Kill Bill,” “Inishmore” represents a decided emphasis on gruesome verisimilitude and sheer theatrical chutzpah over the intellectual ambition Mr. McDonagh displayed in “The Pillowman.” His plays can always be counted for a visceral experience; this time, though, he and Mr. Milam are a little too content to limit this experience to the actual viscera.

The biggest innovation in “The Lieutenant of Inishmore” is the sheer fact that someone’s, anyone’s face can get blown off onstage at any time. This is nothing new in movies, but the limitations of stage effects require a sort of forced decorum. Somebody might get fake-strangled or even take a discreet bullet in the chest, but the rough stuff happens offstage.

Not here: One body after another crumples into a bloody pulp, and barely a square inch of Scott Pask’s grimy set is left unspattered by the end. The scene changes take place in pitch black, accompanied only by Matt McKenzie’s fervent Irish music; the length of the darkness is usually a good indicator of how much gore has been added to the stage.

The dawning realization that any number of people are going to die by a whole new set of grisly rules packs an unexpected wallop. But it also ensures that the audience never gets too close to any of the characters. (The two poor souls trying to create a fake Wee Thomas, played by Domhnall Gleeson and the terrific Peter Gerety, come the closest.) A trio of vengeance-minded baddies may as well have bull’s-eyes painted on their backs, and a budding romance between Padraic and the tomboyish Mairead (Kerry Condon) has more to do with inserting another fraught dynamic – and another gun – into the mix than with creating a fully realized relationship.

Genuine shocks are hard to come by these days, and “The Lieutenant of Inishmore” is a rare specimen indeed in its giggly nihilism and Grand Guignol verve. (“After your son tries to execute you, your opinions do change about him.”) Mr. McDonagh may just reach the seen-it-all youngsters that were presumably eager to swallow up the likes of “Dog Sees God” and “Red Light Winter.” They will absolutely see something they’ve never seen onstage before. Will it be enough?

*** Mr. McDonagh has a busy week. In addition to the “Inishmore” opening, his debut film, “Six Shooter,” is up for an Academy Award for best live-action short on Sunday. It and its four competitors are being screened (along with the animated shorts) at Cinema Village this week.

With its coiled violence and Irish eloquence, the 27-minute film shouldn’t disappoint the playwright’s fans, and two “Inishmore” co-stars – Messrs. Wilmot and Gleeson – are also in the cast.

“The Lieutenant of Inishmore” until April 9 (336 W. 20th Street, between Eighth and Ninth Avenues, 212-239-6200).