Stump was part of three consecutive Southwest Conference championship teams as a quarterback for Texas A&M. He was pressed into duty as a freshman in 1984 after standout Kevin Murray was injured in an early season nonconference game. Although Stump filled in capably completing 94 of his 189 attempts for 1135 yards, he would spend his sophomore and junior seasons on the bench watching Murray break most of the Aggies' passing records. Since the NCAA had granted Murray an extra year of eligibility (considering the '84 year a medical redshirt season), it appeared that Stump would spend his senior year as a backup once again. When Murray decided to leave school early for the NFL draft, Stump had his opportunity.
Because of the loss of Murray and several other key Aggie players after the 1986 season, expectations were not high entering the 1987 campaign. Surprising many, Stump and freshman phenom Bucky Richardson led the Aggies to an unexpected conference championship and an unprecedented third straight Cotton Bowl Classic appearance, a 35–10 victory over Notre Dame and Heisman Trophy winner Tim Brown.
Stump has been the head coach at Atascocita High School since 2012.
Stump has been the head coach at West Brook since 2005. In 2007, he won his second consecutive District 21-5A title by leading his team to a 10-1 record.
Prior to West Brook, he was the head coach at Kelly High School, also in Beaumont. Before coaching in high school, Stump spent six years as an assistant for Mississippi State under his former college coach, Jackie Sherrill as well as three seasons as an assistant at Tulane.