Mamula played college football at Boston College. He redshirted in 1991 and then hurt a shoulder at the beginning of the 1992 season, although he played through it. In 1993, as a junior, Mamula had 84 tackles and 11 sacks as a rush-backer in a 3-4 defense for Boston College. Mamula added another sack in the Carquest Bowl, bringing his season total to twelve. In 1994, his senior year they switched to a 4-3 defense and Mamula was a right defensive end. From that position he had 73 tackles and 13 sacks and four more in the team's 12-7 Aloha Bowl win over Kansas State University, bringing his season total to 17 sacks. For his efforts he was voted All-Big East.
Mamula improved his draft stock tremendously thanks to his showing at the NFL Combine. He was one of the first players to train specifically for the combine drills, performing each drill hundreds of times in the months leading up to the combine. Although that practice is prevalent today, in 1995 most players performed football drills and paid less to attention to the specific drills measured at the combine. Mamula had 28 reps of 225 lb bench presses, which was more reps than the top tackle taken in the draft (Tony Boselli), and his 4.58 40-yard dash time was considered extremely fast for his position. He scored a 49 out of 50 in the Wonderlic Test, which is the second highest score ever recorded by an NFL player. In addition he also had a 38.5 " vertical jump, higher than CB Jimmy Hitchcock.
Also performed the Four-Square run in 7.82#. The pound sign "#" is to not to be confused with the 3-cone drill, which is now in use at the NFL Combine. The Four-Square drill was the drill used in that era. Mamula's 7.82 second drill was only 0.03 second off the best time posted at that combine of 7.79. Additionally, Mamula posted a 40-yard dash time of 4.58 seconds, a vertical jump of 38½ inches, a standing broad jump of 10'5" inches, a 20-yard shuttle of 4.03 seconds and a 4-square run of 7.82 seconds. The previous day he had bench- pressed 225 pounds 26 times. Of the 300 players at the combine regardless of position, the fastest 40 was 4.42, the best vertical jump was 41½, the best standing broad jump was 10'11', the best 20-yard shuttle was 3.90, the best 4-square was 7.79 and the best bench press was 37 reps.
The Philadelphia Eagles traded their first-round draft pick (12th overall), and two second-round selections to the Tampa Bay Buccaneers in exchange for their first-round draft pick (7th overall) and a third round selection. All picks involved in this trade were in the 1995 NFL Draft. The Eagles then selected Mamula, apparently hoping he would fill the void left by Reggie White two years earlier. The Buccaneers went on to draft Warren Sapp with the 12th pick, and traded the pair of second-round picks for the 28th overall pick in the same draft, which they used to get Derrick Brooks. Essentially, the Eagles passed up on two Hall of Famers for Mamula.
Because Mamula's subsequent NFL career was not commensurate with his top combine showing, he is often pejoratively referred to as a "Workout Warrior" and his name is frequently invoked when players go into the combine as relative unknowns and come out as hot properties. Additionally, the first-round pick Tampa Bay acquired in the deal turned into Warren Sapp, who would be one of the cornerstones of the Bucs franchise for a decade and end up in the Hall of Fame. Michael David Smith wrote an article for The New York Times in 2008 refuting these characterizations, noting that scouts were impressed with Mamula's play while he was at BC and arguing that Mamula had an underrated career.
In 77 career games with the Eagles, Mamula had 209 total tackles and 31.5 sacks. His best seasons were 1996 and 1999. In 1996 he logged 8 sacks and in 1999 he had 8½, after recovering from missing the entire 1998 season. He also picked off a pass from Kurt Warner and returned it for a touchdown in the last game of the 1999 season. He was forced to retire after the 2000 season due to injuries. He has been inducted to Boston College's Sports Hall of Fame.