Mims attended Susan Miller Dorsey High School in Los Angeles, California. As a senior, he set the school single season records for sacks and tackles. However, he failed to meet the academic qualifications to attended an NCAA university. Therefore, he chose to attend Los Angeles Pierce College, then Los Angeles Southwest Junior College. After earning better grades, he was recruited by assistant coach A. J. Christoff to the University of Tennessee where he spent two seasons. While at Tennessee, he recorded 90 tackles and 9.5 sacks. In the October 18, 2010 issue of Sports Illustrated, former NFL agent Josh Luchs alleged that he paid Mims 'about $500 a month' during his last year at the University of Tennessee.
Professional career
Mims was selected in the first round of the 1992 NFL Draft. As a rookie, he appeared in 16 games with four starts. During his rookie season, he recorded 53 tackles, 10 sacks, one forced fumble and one fumble recovery as well as recording a safety. In 1993, he appeared in 16 games with seven starts. He recorded 32 tackles, seven sacks, two forced fumbles. For the 1994 season, he started all 16 games. He recorded 35 tackles, 11 sacks, three forced fumbles and two fumble recoveries. In 1995, he started all 15 games he appeared in. He recorded 28 tackles, two sacks, one forced fumble and one fumble recovery. For 1996, he start all 15 games he appeared in. He recorded 20 tackles, six sacks, one forced fumble and one fumble recovery. After spending five seasons with the Chargers, Mims signed as an unrestricted free agent with the Washington Redskins on June 10, 1997. In 1997, his lone season with the Redskins, he appeared in 11 games with seven starts. For the season, he recorded 16 tackles, four sacks and one forced fumble. One year, to the day after signing with the Redskins, Mims re-signed with the Chargers to a one-year contract. In 1998, after returning to the Chargers, he appeared in six games. For the season, he recorded three tackles, and two sacks. On February 8, 1999, he re-signed with the Chargers on a two-year contract. For 1999, he appeared in nine games. For the season, he recorded five tackles. He was released on October 9, and re-signed on October 16. He was released again, for the final time by the Chargers on December 3, 1999. On February 15, 2000 Mims was signed by the Chicago Bears. He was released on August 22, 2000, after missing a practice because he overslept.
During his playing career, Mims had numerous legal troubles. Among them were charges of assault, vandalism, and driving under the influence. He was taken to court more than 20 times for unpaid bills in San Diego County. All of which date to his National Football League career. A career during which he earned almost $6 million. He is reported to have defaulted on a $243,750 house loan during the Chargers' Super Bowl season. He neglected bills for his Mercedes-Benz 600 SEL, attorneys' fees, carpet bills, liquor bills and, at times, child support. In 1995, he was cited by a Superior Court judge for not making monthly payments of $5,000 to a man whose windshield he smashed in a traffic dispute. In 1998, he was convicted of refusing to take a blood-alcohol test after being pulled over on suspicion of driving drunk. In 1999, he pleaded guilty to a misdemeanor assault charge after he hit a man with a belt outside a Del Taco.