Quinn was born in Dublin, Ireland, and moved to the United States with his mother and two sisters in 1988. His first role was as a pool shark in the Richard Marx video Satisfied. He later landed a major role in the John Travolta film Shout (1991), where he shared a screen kiss with Gwyneth Paltrow. He went on to have roles in a number of other movies and television series. His most notable roles were as Becky's husband, Mark, on Roseanne (1988) and half-demon Doyle on the WB's Angel (1999). He died of a heroin overdose in 2002.