During the 1937–1938 season, the Redskins finished 11–5. 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. Mauer became the head coach for the Tennessee Volunteers men's basketball team of the University of Tennessee in Knoxville, Tennessee, for eight seasons between 1938 and 1947. Mauer's Volunteers had significant success, posting an overall record of 127–41 (.756), and winning two Southeastern Conference (SEC) championships (1941, 1943) and two SEC tournaments (1941, 1943). In 1945, John led the team to the Quarterfinals in the National Invitation Tournament (NIT). At the time, the National Invitation Tournament was more prestigious than the NCAA Basketball Tournament. During his time as the Volunteers' head basketball coach, he also worked as the head coach of the Tennessee Volunteers baseball team from 1938 to 1942, and as an assistant football coach for the Tennessee Volunteers football team under head coaches Neyland and John Barnhill from 1938 to 1946. Mauer later served as the head coach for the Army Black Knights men's basketball team of the U.S. Military Academy in West Point, New York, for four seasons from 1947 to 1951, and the Florida Gators men's basketball team of the University of Florida in Gainesville, Florida, for nine seasons from 1951 to 1960. His four Army Cadets teams finished 33–35 (.485); his nine Gators teams compiled a record of 98–102 (.490). While coaching the Gators basketball team, he also served as an assistant coach for the Florida Gators football team under head coaches Bob Woodruff and Ray Graves. 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 died in Knoxville on December 20, 1978; he was 77 years old. He was survived by his wife Grace, their two sons, and their five grandchildren. 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.