Burke attended Marietta High School where he earned three letters in football and track and two in basketball. He was also selected as All-State, All-Central Ohio League, and Running Back of the Year in the Southeast District. His senior year, he rushed for over 1,200 yards and scored 22 touchdowns and was also the placekicker. He was also the state champion in the high hurdles in 1972 and rated as number one junior hurdler in the nation.

His freshman year at WVU, he played tailback, flanker, split end, and defensive safety before settling at defensive back. He had a 6.3 yards per carry average and was the leading punt returner and scored on a 63 yard pass play against Potomac State. He was elevated to varsity the last two games of his freshman year.

He was a versatile athlete who also starred on WVU's track team. He posted a 7.3 clocking in the indoor 60 yard high hurdles and was a member of the "B Brigade" (Burke, Blake, Buggs) that set the top Eastern clocking in the indoor mile relay at 3:17.3 his freshman year. Burke joined fellow footballers Harry Blake and Danny Buggs to set that record.

As a sophomore, Mark started six games and played in the other five. He intercepted one pass and made 52 tackles and also blocked four passes. That year, he also established two WVU hurdle records for the 120-yard high hurdles (14.1) and 440-yard intermediate hurdles (53.5). Going into his junior year, he was listed as the number two left cornerback. That year, he started five games and played in the other six. The following spring he skipped track season to concentrate on spring football drills. As a result going into his senior year he was listed as a starter at free safety after making the move from the corner back position he played last season.