Coming out of Iowa Sate, Braswell joined he BC Lions as a free agent in 1987.  He was released by the Lions before the season started and ended up playing for the Washington Reskins during their strike season in 1987.  BC resigned Braswell in 1988, and he quickly gained a reputation as a very aggressive defensive player, recording an impressive 109 defensive tackles in his rookie season.  Braswell was not destined, hoever, to have a long career in bC, but not because of his play.  In 1989, he was dispatched to Edmonton as part of a deal from the perevious eason when th eLions picked up future HOF quarterback Matt Dunigan from Edmonto for receiver Jim Sandusky.  Besides Braswell, BC sent running back Reggie Taylor, linebacker Gregg Stumon, defensive back Andre Francis and a first round draft pick in 1989 (Leroy Blugh) to Edmonton.

Braswell would play two seasons with Edmonton (1989-90) and was then traded to Ottawa for wide receiver David Williams along with an exchange of first round draft picks in 1991.  Braswell wold play only two games i n the nation's capital before being released in July of 1991.  Later in that same season, he would signe with the Argonauts. Braswell finished out the 1991 season with Toronto and played 11 games in 1992 in double blue.  After not playing in the CFL in 1993, Braswell made a brief return to Ottawa for two games in 1994.