While attending Illinois, his roommate was Illini football great Harold E. "Red" Grange.

Mauer was named Outstanding Athlete and Scholar in the Big Ten Conference as a senior, and graduated from Illinois with a bachelor's degree in 1926.

At Miami, he coached Walter "Smoky" Alston who would go on manage the Brooklyn and Los Angeles Dodgers.

He finished his Miami career with an overall record of 46–80 (.365), leaving Oxford after the 1937–1938 season, and was replaced by Weeb Ewbank.

After his final season as the Gators' basketball mentor, Mauer returned to the University of Tennessee and worked as an assistant coach for the Volunteers football team from 1960 to 1963 under head coaches Bowden Wyatt and Jim McDonald.

Mauer was the first, and to date the only, person to serve as the head coach in the same sport at three different SEC universities.

His winning percentage as the Tennessee Volunteers men's basketball head coach remains the best of the modern era; his winning percentage as the Kentucky Wildcats' head is still among the program's six best of the modern era.