Braswell began his professional career splitting the 2002–03 season in Belgium with Tournai Estaimpuis and in Poland with
Spójnia Stargard Szczeciński. For the 2003–04 season, he moved to Italy to play for Cimberio Aironi Novara. He later signed with the
Miami Heat on October 3, 2005, He subsequently returned to Europe and played seven games for Greek team
Kolossos Rodou before leaving in December 2005. For the 2006–07 season, Braswell moved to Russia to play for Standart Samara reg. Toliatti. Following the conclusion of the Breakers' season, Braswell returned to Europe and joined French team
Limoges CSP. After initially signing with Turkish team Aliağa Belediyesi SK for the 2010–11 season, Braswell instead returned to New Zealand and joined the Breakers for the
NBL season. In April 2011, he helped the Breakers win the
NBL championship. He was subsequently named the
NBL Best Sixth Man. In May 2011, Braswell joined the
Southland Sharks for the
2011 New Zealand NBL season. However, just six games into the season, he suffered a season-ending
Achilles injury which required surgery. He had never previously experienced a serious injury in his basketball career. However, on November 5, 2012, he was released by the Tigers after playing hurt over the first five games. Braswell returned to the Southland Sharks for the
2013 New Zealand NBL season and helped lead them to the
championship. He returned to the Sharks in
2014 and had a 45-point effort in his 50th game. Returning to Southland for a fifth season in
2015, Braswell helped the Sharks win their second title in three years. He retired from professional basketball following the 2015 season, with the Sharks retiring his No. 12 jersey. In 78 career games for the Sharks, he averaged 19.5 points, 3.8 rebounds, 4.8 assists and 2.2 steals per game. ==Coaching career==