The movie was shown Wednesday night at the SXSW Film Festival in Austin.
Gibson became a polarizing figure in Hollywood after making anti-Semitic remarks to a police officer during a July 2006 drunken driving arrest. Audio of Gibson allegedly uttering racial slurs during a heated argument with his ex-girlfriend, Oksana Grigorieva, hit the Internet last summer, further tarnishing Gibson's reputation.
He has since pleaded no contest to battery in the altercation with Grigorieva, the mother of his toddler daughter. Gibson was sentenced to three years probation, a 12-month domestic violence counseling program and community service.
Throughout his various troubles, his longtime friend Foster has repeatedly defended him. She did so again at Wednesday night's screening of "The Beaver."
"I just have to ask everybody, can you see a film and appreciate the artist for his work?" The Hollywood Reporter quoted Foster as saying before the screening. "And if anything, I think anybody who comes to see the film and understands Mel's extraordinary performance in the movie can't go away untouched by his humanity."
The entertainment industry trade newspaper said Foster, co-star Anton Yelchin and screenwriter Kyle Killen attended the screening, while Gibson missed the event.
"If there's a message to the movie," Foster said, "it's that you don't have to be alone. The truth is that the great remedy for that is connection."
In the film, Gibson plays a troubled man who communicates through a beaver hand puppet.
JERMAINE JACKSON: U.S. recording artist and reality TV personality Jermaine Jackson says he is writing a memoir about his late brother Michael.
Touchstone announced Wednesday it will publish "You Are Not Alone, Michael: Through a Brother's Eyes," a book that will cover Michael's personal troubles and career triumphs.
Michael Jackson died June 25, 2009, at age 50. His personal physician is awaiting trial on an involuntary manslaughter charge for allegedly administering lethal levels of anesthesia and sedatives to Michael in an effort to help the eccentric pop star sleep.
"We don't want Michael's life -- or death -- to be an eternal mystery," USA Today quoted Jermaine as saying in a statement.
"This is the truth as we know it. I have read so much about what people think they know about Michael, but this is about what really happened. I hope to make sense of the occasions when the outside world struggled to understand my brother's world. Everyone has said it all about Michael and us. They cannot say anything more. Now it is our turn."
SELENA GOMEZ: Actress-singer Selena Gomez dodged David Letterman's questions about her rumored romance with Justin Bieber during her "Late Show" visit in New York.
During Wednesday's interview, Letterman held up a Feb. 27 photo of Gomez, 18, and Bieber, 17, together at the Vanity Fair Oscar party and asked: "He was your date? You're dating -- are you dating? You're not dating?"
Gomez replied: "It was like a little prom night, wasn't it? Looked like it."
"You guys look very happy there," Letterman remarked. "How long have you known him?"
"Uh, almost, like, two years now," Gomez said.
Letterman then inquired how they met, to which Gomez said Bieber's manager called her mother, who's also her manager.
"Are you dating? You're not dating?" Letterman followed up.
"He's been in my life for so long," Gomez said, "and it's just nice to have someone that understands what you're going through."
Letterman went on to wish Gomez and Bieber luck, to which Gomez said, "Thank you."
GARRISON KEILLOR: U.S. radio personality and author Garrison Keillor says he plans to retire in the spring of 2013.
The 68-year-old host of "A Prairie Home Companion" spoke for the first time about his retirement plans to the AARP Bulletin.
"I am planning to retire in the spring of 2013, but first I have to find my replacement. I'm pushing forward and also I'm in denial. It's an interesting time of life," Keillor told the magazine.
"I sure don't want to make a fool of myself and be singing romantic duets with 25-year-old women when I'm 75. But on the other hand, it's so much fun. And in radio, the lighting is right."