Heading into college, Thompson was rated as a two-star recruit by Rivals.com and the 91st-best fifth year player by Hoop Scoop Online. On November 9, 2006, he committed to playing for Pepperdine University. In his freshman season at Pepperdine, he started 24 of 32 games and averaged 8.1 points and 2.7 rebounds per game. He led the team in three pointers made with 56 and in three-point field goal percentage with 37.3% of his attempts going in. Thompson made a three-pointer in 30 of the 32 games he played. Against Northern Arizona, he scored a season-high 22 points, including five three-pointers. Thompson started 30 of Pepperdine's 32 games in his sophomore season, averaging 9.6 points and 3.5 rebounds per game. He made 35 three-pointers that season, which tied him for the team lead. During the season, he made at least one three-pointer in 21 games. In the season opener, he scored a season-high 25 points against Cal State-Monterey Bay. As a junior, Thompson averaged 11.8 points and 5.0 rebounds per game, en route to being named to the All–West Coast Conference honorable mention team. For the third straight season, he led the team in three-pointers made with 48. He tied his career-high of 25 points against the Utah Utes on December 23, 2009, and was later named the Co–West Coast Conference Player of the Week for his performance against Loyola Marymount, a game in which he scored 22 points and made six of his seven three-point attempts. In his final season at Pepperdine, he averaged 14.6 points per game and 5.9 rebounds per game, both of which led the team. Thompson also led the team in three-pointers made for the fourth consecutive season with 53. For the second straight season, he was named to the All–WCC honorable mention team. Against the Nevada Wolf Pack, he scored a career-high 34 points. On February 2, 2011, he scored 31 points and grabbed 10 rebounds against the San Francisco Dons, becoming the first player from Pepperdine to record over 30 points and grab over 10 rebounds since 2005. Thompson finished his career at Pepperdine with 1,413 points, which is 14th best in school history. He also played in a school record 128 games and his 192 three-pointers made in his career was good enough for fourth highest in school history.
Professional career
2011–12 season
Thompson went undrafted in the 2011 NBA draft. On November 3, 2011, he was selected by the Erie BayHawks in the third round of the 2011 NBA Development League Draft. On December 9, 2011, he signed with the Cleveland Cavaliers. On February 6, 2012, he was waived by the Cavaliers after just five games. On February 10, 2012, he was re-acquired by the BayHawks.
2012–13 season
In July 2012, Thompson joined the New York Knicks for the 2012 NBA Summer League. On September 11, 2012, he signed with the Knicks. However, he was later waived by the Knicks on October 27, 2012. On November 1, 2012, he was re-acquired by the Erie BayHawks. On January 3, 2013, Thompson was traded to the Sioux Falls Skyforce in a three-way trade involving the Rio Grande Valley Vipers and the Erie BayHawks.
2013–14 season
In July 2013, Thompson joined the Minnesota Timberwolves for the 2013 NBA Summer League. On November 4, 2013, the Sioux Falls Skyforce traded Thompson's rights to the Santa Cruz Warriors. On November 19, 2013, he was acquired by the Warriors. During this season at Santa Cruz, Thompson played in the back court with Seth Curry. At the same time, their respective brothers Klay and Steph were playing together in the Golden State back court, in a tandem nicknamed the "Splash Brothers." Correspondingly, Mychel and Seth were dubbed the Splash Brothers of the D-League.
2014–15 season
On November 3, 2014, Thompson was reacquired by the Santa Cruz Warriors. On April 26, 2015, he won the D-League championship with the Warriors.
2015–16 season
On July 16, 2015, Thompson signed with Pallacanestro Varese of Italy. On December 22, he parted ways with Varese after appearing in nine league games and five FIBA Europe Cup games. On February 27, 2016, Thompson was reacquired by Santa Cruz. That night, he made his season debut in a 133–124 loss to the Reno Bighorns, recording 16 points, one rebound and one assist in 23 minutes.
2016–17 season
On November 11, 2016, Thompson was reacquired by the Santa Cruz Warriors.