Career
Mulligan started his senior career playing for Bohemians in 1963. However after only two games he signed for Shamrock Rovers in December 1963. He represented Rovers in European competition 10 times.
In the summer of 1967 he was part of the Rovers team that represented Boston in the United Soccer Association league.
In 1968, they sent him on loan to the Boston Beacons of the North American Soccer League. On 22 October 1969, Mulligan signed for English club Chelsea for £17,500.
He also played in Chelsea"s League Cup final against Stoke City a year later, though they lost 2–1 at Wembley. Mulligan left Chelsea in 1972 for Crystal Palace.
He stayed with the South London club for three years (his personal highlight was scoring two goals in the famous 5-0 victory over Manchester United in 1972).
He signed for West Brom after his spell at CPFC. Mulligan re-joined Shamrock Rovers in 1979, making his final appearance on 24 February 1980. He had his testimonial in August 1980. He then joined Panathinaikos as assistant manager before retiring from the game in 1982.
Mulligan managed League of Ireland sides Galway United (during the 1983-1984 season) and Shelbourne during the first half of the 1985-1986 season.
He also applied to manage the Irish national team, but lost out to Eoin Hand by a single vote. One FAI committee member later said he had voted against Mulligan because he thought Mulligan had thrown a bun at him on a past away trip.
Mulligan occasionally appears as a soccer analyst on Irish television channel TV3.