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, he attended College of the Holy Cross.
In one season career, Mulligan posted a 1–0 record with 13 strikeouts and a 3.63 ERA in 14 appearances, including two starts, one complete game and 44? innings of work.
In 1936, he pitched for Falmouth in the Cape Cod Baseball League.Mulligan died at the age of 72 in West Roxbury, Massachusetts.