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. Listed at 6 ft 4 in (1.93 m), 210 lb., Mulligan batted and threw right-handed.
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 44+2⁄3 innings of work for Boston. In 1936, Mulligan pitched for Falmouth in the Cape Cod Baseball League. He died in 1986 in West Roxbury, Massachusetts at age 72.