Mulligan showed strong musical instincts from his early youth. He played piano and wind instruments with a number of small musical ensembles throughout his school years. Leaving school in 1944, he worked with a number of bands, most notably with Gene Krupa's big band (1946), as an arranger. Shortly after that, Mulligan became involved in a movement to develop a different style of jazz, known as cool jazz. He also had begun to specialize in baritone saxophone and to perform live and on recordings with groups led by such musicians as Miles Davis, Kai Winding, Elliot Lawrence, and Claude Thornhill. In 1952 Mulligan formed his own quartet, which included Chet Baker on trumpet. The group, notable for its lack of a pianist, brought international acclaim to both Baker and Mulligan. During the following decades Mulligan continued to work as a freelance arranger, formed groups varying in size from four to 20 (including the 13-piece Concert Jazz Band of the 1960s), and played throughout Europe and the United States and in Japan. He is considered to be a versatile musician, equally comfortable with many styles of jazz, and one of the more important baritone saxophonists in the jazz idiom.