Beamer was born in Mount Airy, North Carolina, grew up in Fancy Gap, Virginia, went to high school in Hillsville, Virginia, and earned 11 varsity letters in high school as a three-sport athlete in football, basketball, and baseball. He then attended Virginia Tech and was a starting cornerback for three years on the football team, playing in the 1966 and 1968 Liberty Bowls. He graduated in 1969 and attended Radford University for graduate school while serving as an assistant football coach at Radford High School.