Watts spent his first year of high school with Allen Academy in Detroit, Michigan. As a freshman, he averaged 14.1 points and led his team to a 19–3 record. After Allen Academy closed, Watts transferred to Old Redford Academy in Detroit for his next two years. While at the school, he also played with The Family Detroit on the Amateur Athletic Union circuit. In his sophomore season, Watts averaged 25.6 points, 6.2 assists, and 2.8 steals per game and earned Detroit News second-team All-Area honors. As a junior, Watts averaged 26.8 points, 5.6 rebounds, 5.4 assists, and 3.1 steals per game, helping Old Redford Academy to a 19–6 record. He was a Detroit News first-team All-Area pick. Watts was named first-team All-State in each of his first three seasons. For his senior season, Watts transferred to , a boarding prep school in Geneva, Ohio. On January 26, 2019, he scored a career-high 64 points, with 15 three-pointers, in a win over St. Edward High School. Watts, on April 29, played in the Jordan Brand Classic all-star game.
Recruiting
By the end of his high school career, Watts was a consensus four-star recruit and top-40 player in the 2019 class. On September 22, 2018, he verbally committed to play college basketball for Michigan State. Watts had been recruited by Michigan State head coachTom Izzo since eighth grade.
College career
Watts started his first career game on November 5, 2019, in place of the injured Joshua Langford against the Kentucky Wildcats. He was held scoreless, going 0–4 from the field while picking up 2 assists in 22 minutes played in the 62–69 loss. Five days later, against Binghamton, Watts collected his first career points, finishing with 5 in 23 minutes as the Spartans demolished Binghamton 100–46. On November 18, 2019, Watts recorded a then career-high 11 points to go with another career-high 7 total rebounds as the Spartans routed Charleston Southern 94–46. Watts suffered a leg injury in December 2019 and was forced to miss some time. At the time, he was averaging 6.5 points per game. On February 11, 2020, Watts scored a career-high 21 points in a 70–69 win against Illinois. He tied that career-high of 21 points, leading the team in scoring on February 25, 2020 as the Spartans won against the higher ranked Iowa Hawkeyes, 78–70. Watts played a crucial role in the Spartan's game against Penn State on March 3, as they came back from a 15 point deficit at half to win by 8. He put up 18 points, second on the team that night. On March 8, Watts finished second on the team with 19 points in a 80–69 win over the Ohio State Buckeyes. At the close of the regular season, Watts was named to the Big Ten All-Freshman Team.
Watts was given the nickname "Rocket" while playing football at age five. His father Mark Sr. originally owned the nickname for the speed he displayed while playing high school football.