Just about everything you’ve heard about The Beaver is true.

Yes, this much-buzzed-about indie production – which had its world premiere Wednesday evening in Austin at the SXSW Film Festival – is the latest directorial effort of Oscar-winning multi-hyphenate Jodie Foster.

Yes, it stars Mel Gibson as a harried business executive and family man who suffers a psychological meltdown and slips into a near-catatonic depression.

And yes, the movie’s plot kicks in when the executive reaches a point where he can communicate freely with loved ones and employees only by speaking in a thick, growly brogue through a beaver hand puppet.

But no, regardless of what you may have heard that might indicate otherwise, The Beaver is not – or at least isn’t intended to be – a comedy.

To be sure, you can’t help but giggle a bit during the early scenes, when the deeply troubled Walter Black (Gibson) ratchets up from morose to manic while getting in touch with his inner beaver. Mind you, the guy doesn’t attempt anything like ventriloquism – he simply lapses into gravelly beaver-speak while flexing the puppet in his hand. But that only makes his role-playing behavior all the more bizarre.

And at first, it’s more than mildly amusing to see how that behavior befuddles his wife (Foster) and their two sons, and discombobulates his second-in-command (Cherry Jones) and other workers at his toy manufacturing company.

But, to reiterate, The Beaver is not a full-scale laugh riot. Rather, it’s intended as a seriously sensitive psychological drama about a man who’s driven to extremes to snap himself out of a debilitating funk. And when, ultimately, Walter literally comes to blows with the hand puppet… Well, let’s put it this way: You’re not supposed to laugh.

In recent weeks, Foster has been on location in Paris, filming Carnage with co-stars Kate Winslet, Christoph Waltz and John C. Reilly for director Roman Polanski. But she took time out to fly all the way to Austin for Wednesday evening’s premiere screening – and to tell the capacity crowd at the Paramount Theatre that The Beaver is no laughing matter.

“I’m hoping to get the word out,” she said, “that this is a thoughtful movie that will require people to think a little bit when they come to the movie theater.”

It will be a difficult movie to market, Foster conceded. And while she nimbly avoided directly addressing the issue, she strongly hinted it doesn’t help that her leading man lately has been involved in more embarrassing off-screen misadventures than any actor this side of Charlie Sheen.

“I feel incredibly grateful to have [Mel Gibson’s] performance in this movie,” Foster said. In almost the same breath, however, she admitted that plans to open The Beaver months ago were put on hold after “all sorts of things that were out of our control came into play… All sorts of stuff happened after the film was finished that sort of threw our release into a crazy pattern.”

Gibson, it should be noted, was conspicuous by his absence at Wednesday’s world premiere. So it was up to Foster – with a little help from Beaver scriptwriter Kyle Killen, an Austin resident, and actor Anton Yelchin, who co-stars in the film – to deal with the post-screening Q&A. She wore sunglasses for the occasion – not to look tres cool, she insisted, but to disguise a minor eye infection.

“Actually,” she quipped, “I’m afraid if I took the glasses off, all of you might turn into vampires or something.”

Gibson’s undeniably potent performance – and his unavoidable off-screen misbehavior – may dominate most press coverage of The Beaver. It’s worth noting, though, that the movie actually tells two contrasting yet interconnected stories.

In counterpoint to Walter’s ongoing struggle to return to normalcy, there is the drama of Porter (Yelchin), Walter’s oldest son, who has identity problems of his own. Specifically, he’s a master at ghostwriting term papers for fellow students. For the right price, he can convincingly mimic the “voice” of anyone who needs his service. Trouble is, Porter, like his dad, finds it difficult to speak for himself.

Striking the perfect balance between these two storylines was “the biggest struggle of my professional life,” Foster said. But it all worked out in the end – for both Foster and the characters in her film.

“Life is full of half-comedy and half-tragedy,” she said. “And the only way to get through it is to know that you’re not alone, that there’s someone there for you.”

Even if that someone is a beaver hand puppet.