Butrick was born in Gainesville, Florida and was an only child. He graduated in 1977 from Tamalpais High School in Mill Valley, California. He attended the California Institute of the Arts for acting, but was dismissed from the school.
His first screen role was as a rapist in two 1981 episodes of the police drama Hill Street Blues.
He was cast as John "Johnny Slash" Ulasewicz, a major supporting character in the 1982 teen sitcom Square Pegs, which received critical praise but was cancelled after 19 episodes (one season). The character was described by one critic as an "apparent (but never declared) gay student."
While Square Pegs was in pre-broadcast production, Butrick was cast to play David Marcus, the physicist son of James T. Kirk (William Shatner) and his former lover Carol Marcus (Bibi Besch), in Star Trek II: The Wrath of Khan. He continued the role in the follow-up film Star Trek III: The Search for Spock, in which the character was killed. He later appeared as T'Jon, the captain of a cargo vessel rescued by the crew of the Enterprise in "Symbiosis", a 1988 episode of Star Trek: The Next Generation.
Meanwhile, he appeared in the 1982 comedy film Zapped!, the 1988 horror film Fright Night Part 2, and as Barbara Hershey's hillbilly son in the 1987 drama Shy People. He had a variety of guest roles in television series and television movies.
He received critical praise from Time magazine for his performance at the Los Angeles Theatre Center in the play Kingfish, in which he played a ditzy, petulant muscle-boy prostitute. It was his last acting role.
Butrick died of toxoplasmosis, complicated by AIDS, on March 17, 1989, at the age of 29. He has at least two panels dedicated to him as part of the NAMES Project AIDS Memorial Quilt, both referencing his role as David Marcus.
The 2008 release of Square Pegs on DVD included a featurette dedicated to Butrick, in which his co-stars, including Jami Gertz and Sarah Jessica Parker, and show creator Anne Beatts, paid tributes to and recounted anecdotes about Butrick.
Butrick's Star Trek III co-star Robin Curtis offered similar praise on the DVD commentary for that film. Director Nicholas Meyer, who had directed him in Star Trek II, included a scene in Star Trek VI: The Undiscovered Country (filmed after Butrick's death), in which Captain Kirk puts a photograph of his murdered son on his desk.
Some sources state that Butrick was gay. Kirstie Alley, his co-star in Star Trek II, identified Butrick as being bisexual.