[4][5] After college, he began working in theatre, making his debut as a stage manager and performer on Broadway in All the Way Home in 1960.

Mulligan made a brief, uncredited appearance in the 1963 film Love with the Proper Stranger, which was directed by his elder brother.

Another notable TV appearance was on the I Dream of Jeannie episode "Around the World in 80 Blinks", as a navy commander accompanying Major Nelson (Larry Hagman) on a mission.

Mulligan's most notable film role was as General George Armstrong Custer in Little Big Man, whom he portrayed as a borderline psychotic.

Mulligan's best-known roles in television were as Burt Campbell in the sitcom Soap (1977–81), for which he won a Best Actor Emmy Award, and as Dr. Harry Weston in the NBC series Empty Nest, a spin-off of The Golden Girls in which his character had appeared in a couple of episodes.

He also played Secretary of State William Seward in Lincoln (1988), a TV movie based on Gore Vidal's novel.

Lasting for only six episodes, it was a loose adaptation of the popular BBC series The Fall and Rise of Reginald Perrin.

Mulligan lent his voice to Disney's 1988 animated film, Oliver & Company, as the oafish Great Dane named Einstein.