Thigpen was a three sport star at Aucilla Christian Academy near Monticello, FL. As a member of the baseball team he played for longtime Aucilla coach, Ray Hughes. A pitcher and shortstop in high school, he led the Warriors to the 1981 Class A state championship game. He played two years at Seminole Community College, after which he moved on to pitch and play the outfield for Mississippi State University and coach Ron Polk. Among his teammates were future major-leaguers Will Clark, Rafael Palmeiro and Jeff Brantley. Thigpen was part of MSU's 1985 College World Series team, recording a.305 batting average and saving seven games during the season. Thigpen was selected by the Chicago White Sox in the fourth round of the 1985 amateur draft. He made the major leagues the next August and moved into the White Sox's closer role. After two straight 30-save seasons, Thigpen had the best season of his career in 1990, setting the then-major league record of 57 saves. He also maintained a 1.83 ERA and was named to the AL All-Star team. He also blew eight saves that season, including two three-run leads. He later began to battle injuries, starting with a back problem developed after the 1990 season, when some players went on an exhibition tour of Japan. Thigpen's effectiveness waned and he was supplanted in the closer role by Roberto Hernández. During the season, Thigpen was traded to the Philadelphia Phillies for José DeLeón, and pitched in the NLCS and World Series for Philadelphia. The following season, he signed with the Seattle Mariners, who released him on April 29. He joined the Fukuoka Daiei Hawks and attempted to return to the majors in 1996, only to be derailed by back problems, which ended his career. Thigpen's 201 career saves rank him 46th on the all-time saves list.
Post-baseball injury
In 2003, Thigpen was leaving a Stanley Cup playoff game at the St. Pete Times Forum when he tripped and fell on the stairs, triggering massive internal bleeding. "He had about a gallon of blood in his abdomen", said Dr. Kevin Hirsch, a trauma surgeon at Bayfront Medical Center who operated on Thigpen. "He had significant bleeding in and around his pancreas and kidney that we had to go in and stop." Thigpen spent a week in the hospital and recovered.