Roy is an Army brat who was born at Fort Lewis, Washington. His father was a soldier in the U.S. Army. His family lived in Fort Eustis, Virginia from 1989–1996 before moving to Killeen, Texas, when Miller was in middle school. Miller was a star at Shoemaker High School before moving on to the University of Texas at Austin. Miller was an All-American, two-time All-State and three-time All-District performer at defensive tackle and also played some offensive tackle. The All-Area Defensive MVP recorded 111 tackles with 10 sacks, 17 stops for loss, 19 pressures, six pass break-ups and two fumble recoveries, returning one 43 yards for a touchdown as a senior at Shoemaker. In three seasons, the team captain collected 264 tackles with 24 sacks. Roy was a prep All-American who earned practice MVP honors at the U.S. Army All-American Bowl.

After his rookie season with the Steelers, Bleier was drafted into the U.S. Army on December 4, 1968, during the Vietnam War.[8] He volunteered for duty in South Vietnam and shipped out for Vietnam in May 1969 assigned to Company C, 4th Battalion (Light), 31st Infantry, 196th Light Infantry Brigade and assigned as a squad grenadier operating a 40mm M79 grenade launcher. On August 20, while on patrol in Hiep Duc, Bleier was wounded in the left thigh by an enemy rifle bullet when his platoon was ambushed in a rice paddy. While he was down, an enemy grenade landed nearby after bouncing off a fellow soldier, sending shrapnel into his lower right leg.[9] He lost part of his right foot in the blast as well.[10][11] He was later awarded the Bronze Star and Purple Heart. His rank was Specialist 4.