Mulligan studied at Fordham University before serving with the United States Marine Corps during World War II. At war's end, he obtained work in the editorial department of the New York Times newspaper but left to pursue a career in television.

Employed by the CBS network, Mulligan began his television career at the bottom of the ladder, working as a messenger boy. He worked his way up, learning the business to where in 1948 he was directing important dramatic series. In 1959 he won an Emmy Award for directing The Moon and Sixpence, a made-for-television production that marked the American small-screen debut of Sir Laurence Olivier.

In 1960 Robert Mulligan directed his first motion picture and two years later received wide acclaim and Academy award and Directors Guild of America nominations for To Kill A Mockingbird. In 1972 he would be nominated for a Golden Globe Award for Best Director and another Directors Guild Award for the highly successful Summer of '42.

He is the brother of actor Richard Mulligan who is best remembered for his television roles of Burt Campbell in the sitcom Soap and of Dr. Harry Weston in Empty Nest.