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One might have a instinctive reaction to dismiss “The Beaver,” Jodie Foster’s weird comedy-drama starring Mel Gibson as a clinically depressed businessman who finds a sort of voice through a ragged, obnoxious hand puppet. But that would be a mistake. It’s hardly a perfect picture—and one can certainly dispute writer Kyle Killen’s decision to go soft in the last reel—but it’s an intriguingly unusual one.

What punch the picture possesses comes largely from Gibson, who gives a powerhouse turn as Walter Black, whose descent into a perpetual funk has not only precipitated the near-collapse of the family toy business but alienated his wife Meredith (Foster) and high-school son Porter (Anton Yelchin), though his younger son, tyke Henry (Riley Thomas Stewart) still idolizes him. The night that Meredith finally forces him to leave the house, Walter finds the beaver puppet in a dumpster, and when he tries to kill himself, the thing intervenes to save him.

But the beaver—which for some reason speaks in a voice resembling Michael Caine’s—is no happy helpmate. It’s an aggressive, pushy entity that essentially takes over Walter, who passes it off as a “prescription puppet” to get Michelle to take him back. Henry is overjoyed, and the puppet even reinvigorates the Black business by proposing a woodcarving kit that becomes a sensational hit, and Walter himself a media star and pop culture icon, since he gives interviews through the beaver. The only person distressed by Walter’s strange quasi-recovery is Porter, who’s so terrified that he might be fated to follow in his father’s psychological footsteps that he intently keeps track of traits he shares with him.

Porter has also developed some troubling habits of his own, in particular a business writing papers for other students that’s successful because he can get into their heads and write convincingly in their voice (though frankly that wouldn’t seem all that helpful in composing “A” work for “D” students). A good deal of “The Beaver” is actually devoted to the relationship the kid develops with class valedictorian Norah (Jennifer Lawrence), who hires him to write the speech she’ll deliver at graduation. She proves to have family problems, too, and though it brings Porter a measure of contentment the link between them will eventually cause problems.

The amount of space given over to this schoolyard romance actually begins to overshadow Walter’s story and throws the movie out of balance, however nicely Yelchin and Lawrence play it. But the central plot line is garbled in any event. Early on it’s played as dark comedy, but then it turns into a rather labored satire of the culture of celebrity and capitalism, before turning gooey and sentimental in the last reel, when the script strains for a conventional happy ending. The result is a tonal inconsistency that starts in Killen’s script but is accentuated by Foster’s uncertain direction (her on-screen performance, moreover, is bland).

Had the writer and director possessed more courage, they might have played out the psychological implications of their story to the end and wound up with something akin to a grownup analogue to “Donnie Darko.” But instead “The Beaver” pretty much cops out, replacing a Cronenbergian sense of desolation with a dose of hopefulness that seems calculated rather than earned.

The result is a flawed, erratic comedy-drama that nonetheless remains fascinating because of Gibson’s frenziedly committed performance—which, because of his own recent personal history, is all the more compelling.