Stinchcomb attended the University of Georgia, where he played for the Georgia Bulldogs football team from 1995 to 1998. He was a first-team All-American selection at tackle in 1997, and was recognized as a consensus first-team All-American following the 1998 season.
Stinchcomb was selected as the 18th pick of the first round in the 1999 NFL Draft to the Oakland Raiders. He was, however, largely unable to unseat Barry Sims, the player he was drafted to replace, at left tackle for the Raiders. This led to his move inside the offensive line, to both guard and center. He started at left guard during his only healthy season with Tampa Bay in 2004.
In 2009, Matt was named to the University of Georgia's Circle of Honor, the highest level of distinction for any UGA student-athlete. He also represented Georgia in being named to the 2009 class of "SEC Legends" which was recognized during pregame of the SEC Championship Game.