Purcell studied at Memphis State University for a year before moving to the University of Tennessee . There he won the double title in 1980 at the NCAA championships on the side of Rodney Harmon . In the same year he reached the final of Indianapolis and the semifinals of the Japan Open . 1981 was his most successful year on the ATP World Tour , he was able to win three individual titles. In addition, he was in a double final for the first time. The following year he won the double titles of Delray Beach and Munich and was in the individual finals of the tournaments in Los Angeles and Boston . In 1983 he was able to win another double title in Vienna and was in the individual finals in Vienna and at the Monte Carlo Masters .
In 1985 he was operated on on his right elbow and had to sit out for several months. He then played on the ATP Challenger Tour and reached the Raleigh final . In 1987 he won his fourth and final double title with Tim Wilkison . He reached his highest ranking in the tennis world rankings in 1980 with position 21 in singles and 1984 with position 47 in doubles.
In singles, his best result in a Grand Slam tournament was the quarter-finals Wimbledon 1983. In the doubles competition, he reached the quarter-finals of the French Open in 1981 , the second round of Wimbledon and three times the second round of the US Open .
Purcell got into the minds of German tennis fans with his victory against Boris Becker at Hamburg's Rothenbaum in September 1986.
After the end of his professional career, he became the head coach of Murray State University .