Mueller was drafted by Detroit in 1941, but he left the team to perform military service in World War II. He returned to baseball in 1945 and was a part of the Tigers' championship team that defeated the Chicago Cubs in the World Series.
Mueller went 6-8 with a 3.68 ERA in 1945 for Detroit. On July 21 against the Philadelphia Athletics, he pitched 19.2 innings in a game that was called after 24 innings with the scored tied 1-1. The hurler gave up 13 hits, struck out six and walked five in those 19.2 innings.
Mueller left baseball after that season and returned to his hometown of Belleville, Illinois, where he remained for the rest of his life. He is survived by a wife and three son.