Mulligan was born in Queens and started on the piano before learning the various saxophones. His first work was as an arranger for Gene Krupa and Claude Thornhill. Mulligan's first baritone playing was on Miles Davis’ “Birth of The Cool”, which led to work for Stan Kenton. Mulligan’s breakthrough came when he played with Chet Baker, and their special rapport without piano was widely lauded. However, Mulligan’s sextet with saxophonist Zoot Sims and trombonist Bob Brookmeyer would prove equally successful. Later Mulligan worked with orchestras, collaborating with composers Andre Previn and Astor Piazzolla. Mulligan continued to perform and record until late in his life, including work for film and theatre. He passed away aged 68.