Vawter was born in Latham, New York, to Matilda (Buttoni) and Elton Lee Vawter. His maternal grandparents were Italian. Vawter was a graduate of Siena College where he performed in Little Theater productions.
He was a member of The Performance Group -- from which The Wooster Group emerged in 1980. With The Performance Group Vawter performed in 'Mother Courage and Her Children' (Bertolt Brecht), 'The Marilyn Project' (David Gaard), 'Cops' (Terry Curtis Fox), and 'The Balcony' (Jean Genet) -- all directed by Richard Schechner at The Performing Garage or its companion theatre, The Envelope.
In addition to his work with The Wooster Group, Vawter appeared inseveral films, generally playing small but memorable character roles. He also performed in theatre pieces by Richard Foreman, Jeff Weiss, Mabou Mines, and The Performance Group.
In his 1992 work for the stage, Vawter explored the themes of sexual identity in Roy Cohn/Jack Smith , a series of two monologues that contrast the characters of two gay men who died of AIDS. The Jack Smith section was a recreation of Smith's performance "What's Underground About Marshmallows?" and the Roy Cohn section was written by Gary Indiana. It was directed by Greg Mehrten and created with Clay Shirky and Marianne Weems . The piece was released as a film directed by Jill Godmilow in which the sections were intercut.
Vawter's last piece of work, considered his artistic testament, the Philoktetes-variations written by John Jesurun on his request, was performed while the actor was dying of HIV/AIDS. Based on the story about Philoctetes, the ancient Greek warrior whose wound smelled so intolerably noxious that he was banned to the uninhabited island of Lemnos and abandoned by his comrades-in-arms on the way to Troy, it has consequently also become a metaphor for AIDS, with Philoktetes as a plagued outcast.
Vawter embodied Philoktetes three times in Jan Ritsema's triptych in the Brussels' Kaaitheater in 1994, using his own body naked and covered with purple Kaposi rash, thus making the connection between the performance's "here and now" and the story's "there and then" as well as between life and death, subject and object in his first audience address when he said that he was suffering from AIDS: "I am dying, I am on my way to the grave but am just doing this performance on the way".
Vawter died at the age of 45, of a heart attack in-flight on a commercial plane from Zürich to New York.