Joseph Ignatius Mulligan [Big Joe] (July 31, 1913 - June 5, 1986) was a pitcher in Major League Baseball who played briefly for the Boston Red Sox during the 1934 season. Listed at 6' 4", 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 44⅔ innings of work.
Mulligan died at the age of 72 in West Roxbury, Massachusetts.