Mulligan started his playing career in the 1940s with the Illawarra Rugby League's Port Kembla club. In 1945 he joined the previous season's NSWRFL grand finalists, Newtown. Mulligan was first selected to represent New South Wales in 1946 against Great Britain. He was then selected to represent Australia for the first time, also against the British in the first test match, becoming Kangaroo No. 227.[3] He also played in the third Test, losing The Ashes to the Lions.
Mulligan returned to Country New South Wales in 1947, captain-coaching Bowral's club to a Group 6 Rugby League first-grade premiership in addition to continuing representative duties with New South Wales and Country NSW.
In 1948 Mulligan returned to Newtown. He was selected to go on the 1948 Kangaroo tour, playing in all five test matches against Great Britain and France. Mulligan again represented New South Wales and toured New Zealand with the Australian team in 1949, missing his club Bowral's grand final loss. He signed to play in Sydney once again with St. George from 1950, continuing to represent New South Wales as well as Sydney that season. He was selected to represent Sydney against France during their 1951 tour of Australasia in a match that ended in a 19-all draw. He also played his last test match against France during their tour. Mulligan successfully coached the Captains Flat Redmen to successive premierships in the Group 8 competition in 1952 and 1953 before returning to the Illawarra.
Mulligan died in 2000, 32 days before his 74th birthday.[4]
In 2008, the Newtown Jets club's centenary year, they named their 'Team of the Century' with Mulligan at lock forward.[6] In addition the Illawarra Rugby League named him at lock in their team of the century.[7]