Davis was born in Eastern Washington in Palouse on September 6, 1932. His family later moved to neighboring Oregon and Davis lists Independence, Oregon, as his hometown. Mouse gained his nickname from older brother Don while a freshman shortstop on the Central High School team in neighboring Monmouth, Oregon. Despite his 4'10" (1.47 m) stature at the time, Mouse already excelled at sports. In 1955, he graduated from the Oregon College of Education (now Western Oregon University) in neighboring Monmouth. There he played quarterback and halfback on three straight championship teams from 1952–54 under Coach Bill McArthur. Davis also played basketball and baseball at the college.