Shamet was born on March 13, 1997 in Kansas City, Missouri to single mother Melanie Shamet. His maternal grandfather is of Lithuanian descent. His mother went to Boise State University on a volleyball scholarship. His uncle Tyler was a positive influence in his life growing up, and his extended family also provided support in his development. Shamet began playing basketball at the age of two. When he was in middle school, his family went bankrupt after the mortgage increased and lost the apartment. Shamet attended Park Hill High School in Kansas City, where he was coached by David Garrison He was a student in the Advancement via Individual Determination college preparatory program.
College career
Shamet played three games in his freshman season before having to redshirt the season due to a foot injury. In January 2017, he became the point guard for the Shockers. In his redshirt freshman season, Shamet averaged 11.4 points and 3.3 assists per game. He was named to the First team MVC All-Conference and MVC Freshman of the Year. Following the season Shamet had surgery to repair a stress fracture on his foot. Coming into his sophomore year, Shamet was named to the Preseason First Team All-AAC and was one of fifty players named in the Preseason Wooden Award watch list. He was one of only two sophomores to be selected for the 2018 Wooden Award Midseason Top 25 list. Shamet scored a career-high 30 points to help Wichita State beat Oklahoma State 78-66 on December 9, 2017. Shamet led the AAC in several categories, including assists per game, true shooting percentage, and offensive box plus/minus. He also helped lead the Shockers to the NCAA Tournament each season he played. He averaged 14.9 points and 5.2 assists per game as a sophomore. Following the season he declared for the 2018 NBA draft.
Shamet was taken with the 26th pick in the 2018 NBA draft by the Philadelphia 76ers. In the 2018 preseason, Shamet averaged 8.8 points per game, with an 18-point performance in a 120–114 victory over the Dallas Mavericks in China. Shamet scored a career-high 29 points off the bench on January 8, 2019, in a home victory over the Washington Wizards, including a Sixers rookie record 8 three-pointers.
On February 6, 2019, Shamet was traded to the Los Angeles Clippers. In his first game with them, he scored 17 points, 13 of which were in the 4th quarter, in a comeback from 28 down against the Boston Celtics. On April 15, in Game 2 of the first round against the Golden State Warriors, he scored 12 points and the game winning 3-pointer in a 31-point comeback leading to a 135–131 Clippers victory. On 4 July 2020 he tested positive for COVID-19.