Mueller's career was interrupted while he served in the military during World War II, causing him to miss the 1943 and 1944 seasons.

[1] Mueller first played professionally in 1939, appearing in 16 games for the Class D Alexandria Aces of the Evangeline Baseball League.

In 1941, he appeared in 103 games for the Class D Jonesboro White Sox of the Northeast Arkansas League, compiling a .278 batting average.

[5] His contract was purchased by the White Sox when outfielder Taffy Wright had to report for military duty.

[2] Mueller served in the United States Navy from December 1942 through July 1945,[7] thus missing the 1943 and 1944 baseball seasons.