Turpin's father Jack, a businessman, was a collegiate player at Rice University and is a member of the Texas Tennis Hall of Fame.

[2] As a high school senior in 1978, he won the USTA Interscholastic Tennis Championships in both singles and doubles (the latter win was with Brad Stoffel, a St. Mark's teammate).

On the Grand Prix circuit he had his best performance in the 1984 Bristol Open, where he made the quarter-finals, with wins over Mike Leach, Emilio Sánchez and fourth seed John Fitzgerald.

The tournament coincided with Wimbledon qualifying, so Turpin was often required to make the trip between London and Bristol to play two matches in a day.

He left in 1996 to become president of oil and gas investment company, Hallmark Energy, a firm founded by his father, Jack Turpin.