Sutton was born in Clarksville, Tennessee, in 1923. When he was eight years old, his father took a position as a linotype operator at the Nashville Tennessean in Nashville. While growing up in Nashville, he developed an interest in acting, earning his first role at the age of nine. He later commented, "The first time I walked out on a stage, I had a warm feeling. I knew then I wanted to be an actor."

After Sutton graduated from East Nashville High School, he returned to Clarksville to become a radio disc jockey, then enlisted in the United States Army during World War II, and after basic training, was sent to the South Pacific, taking part in 14 assault landings.