His father played basketball for Jacksonville University from 1976 to 1978,[2] and was selected by the Buffalo Braves[1] in the 8th round of the 1978 NBA draft.

In 2006, he led Mitchell's basketball team to the TSSAA Class AA finals against Liberty Technology Magnet High School.

After the trade of Kyle Korver, Young played more minutes and alternated with Reggie Evans in the starting lineup.

[12] On February 21, 2014, Young set a career high with 29 field goal attempts, going on to record 30 points, 13 rebounds, 6 assists and 7 steals in a 112–124 loss to the Dallas Mavericks.

[13] Young finished the 2013–14 NBA season with career highs in points, steals, assists, three-pointers made, and games started.

[18] On February 3, 2016, he recorded 16 points and 14 rebounds against the Indiana Pacers, setting a new single-season career high with his 22nd double-double.

[19] On July 7, 2016, Young was traded to the Indiana Pacers in exchange for the draft rights to Caris LeVert.

[26] Following a mediocre first season where Young struggled from the field, the veteran played better and more effectively during his second season with the Chicago Bulls, with strong inside play combined with good shooting from the field, good defense and strong all around abilities.

[citation needed] On August 11, 2021, Young, Al-Farouq Aminu, and several draft picks were traded to the San Antonio Spurs in exchange for DeMar DeRozan.

[29] On February 8, 2024, Young was traded alongside Dennis Schröder to the Brooklyn Nets in exchange for Spencer Dinwiddie,[30] but was waived that day.