Mitchell graduated from Stanford University and was voted three times for the All-American selection. He was the 1977 NCAA tennis champion . In the same year he won the NCAA title with the team, which was defended the following year. Mitchell competed here in doubles on the side of John McEnroe .
He became a tennis professional in 1979 and was able to win his first ATP double title with McEnroe in Brisbane the following year . In the following two years he won another double title. 1984 was his most successful year. At the side of Francisco González , he won three double titles, including the Masters tournament in Cincinnati . In addition, he won his only individual title on the ATP World Tour in Melbourne through a final victory against the favored Pat Cash , after losing to Marty Davis in his first final in Cleveland the year before . In total, he won seven ATP double titles in the course of his career, and another three times he was in a double-final. He reached his highest ranking in the tennis world rankings in 1985 with position 53 in singles and 1984 with position 30 in doubles.
His best individual results in Grand Slam tournaments were two third round participations at the Australian Open. In the doubles competition he stood alongside Kevin Curren in the semifinals of the US Open in 1986 , where they were defeated in five sets against Mats Wilander and Joakim Nyström .