Purcell grew up in Murray, Kentucky, and played in the Kentucky State Tennis Tournament as a fifth-grader, and won two state doubles crowns with older brother Del as a middle schooler. He made the state singles finals three straight years, winning as a senior.
Purcell graduated Murray High School and went on to Memphis State University (now the University of Memphis), where he played for one year. He transferred to the University of Tennessee, where in 1980 he won an NCAA doubles championship with teammate Rodney Harmon.
Purcell made his first splash on the professional circuit in the summer of 1980. As a wild card entrant at the Washington (D.C.) Star Tournament, he upset top-ranked Eddie Dibbs. Two weeks later, he qualified for a spot in the U.S. Clay Courts. There, he beat Hank Pfister and top-10 ranked Harold Solomon before falling in the finals to José Luis Clerc. Purcell saw his Association of Tennis Professionals (ATP) ranking soar from the 300s to the top 40 and was crowned 1980 ATP Rookie of the Year.
The next year he played at Wimbledon, the first of six appearances (1981–85, 1987) on the famed grass courts. He reached the quarterfinals in 1983, beating Tim Wilkison, Stuart Bale, Andreas Mauer and Brian Gottfried before falling to eventual runner-up New Zealand's Chris Lewis 6–7, 6–0, 6–4, 7–6 in the quarterfinals.
Purcell also was a fixture in other Grand Slam events during the 1980s, playing in the US Open 10 times (1978–87) where he recorded victories over Stan Smith, Andrés Gómez and Ilie Năstase, among others. During this time, he was part of a rare match that saw the eventual loser win two sets 6-0. This occurred during his third round loss to José Luis Clerc 6-3 0-6 0-6 6-4 6-3 in the 1981 US Open. He competed in the French Open six times (1981–84, 1987–88) where he twice reached the round of 16 in singles and in 1981 reached the doubles quarterfinals with Vincent Van Patten.
Another career highlight was beating Ivan Lendl and Fernando Luna at Boston in 1982 before falling in the final to Guillermo Vilas.
Injuries to his elbow from a car accident and a pulled stomach muscle slowed his career in 1985 but a year later, he beat Boris Becker in the German Open for another milestone singles victory.
Purcell won three ATP singles titles in 1981, at Atlanta, Tampa and Tel Aviv. He also teamed to claim four doubles titles, at Delray Beach (1982 with Chip Hooper), Munich (1982 with Eliot Teltscher) and Vienna (1983 with Stan Smith and 1987 with Tim Wilkison).
Ace Authentic produced a line of trading cards called "Heroes & Legends" that included Purcell at his best.
Purcell is the head tennis coach at Murray State University, a post he took in 1996 succeeding his father, hall of fame coach Bennie Purcell. He led Murray State to back-to-back Ohio Valley Conference titles in 2001 and 2002 and was named OVC Coach of the Year both seasons.
Mel Purcell was still enjoying matches on the Jimmy Connors Champions Tour in his 40s, where he played against and sometimes beat Jimmy Connors, Björn Borg, and John McEnroe.
Mel hosts a tennis camp every summer for kids and teens and he enjoys showing them his techniques.