Joseph Ignatius Mulligan (July 31, 1913 – June 5, 1986), nicknamed "Big Joe", was a pitcher in Major League Baseball who played briefly for the Boston Red Sox during the 1934 season.

A native of Weymouth, Massachusetts, Mulligan attended the College of the Holy Cross.

In his lone major league season, he posted a 1–0 record with 13 strikeouts and a 3.63 ERA in 14 appearances, including two starts, one complete game and 44⅔ innings of work for Boston.

In 1936, Mulligan pitched for Falmouth in the Cape Cod Baseball League.

This biographical article relating to an American baseball pitcher born in the 1910s is a stub.