As a child, Murphy was a loner with mood swings and an explosive temper. He grew up in northeastern Texas around the towns of Farmersville, Greenville, and Celeste, where he attended elementary school. His father drifted in and out of the family's life and eventually deserted them. Murphy dropped out of school in fifth grade and got a job picking cotton for a dollar a day () to help support his family; he also became skilled with a rifle, hunting small game to help feed them. After his mother died of endocarditis and pneumonia in 1941, he worked at a radio repair shop and at a combination general store, garage and gas station in Greenville. Hunt County authorities placed his three youngest siblings in Boles Children's Home, a Christian orphanage in Quinlan. After the war, he bought a house in Farmersville for his eldest sister Corinne and her husband, Poland Burns. His other siblings briefly shared the home.