Murphy was born in Durham, North Carolina, to his mother, Albeda, and father, Kenneth Murphy Jr.[1] He played high school basketball at Cary Academy in Cary, North Carolina, where, as a senior, he averaged 24.7 points and 7.4 rebounds per game while shooting 49.4% from the floor.

He ranked fourth in Conference USA (C-USA) in three-point field goal percentage (42.1%) and 14th in 3-pointers made per game (2.0).

Coming off the bench, Murphy scored 21 points while shooting 7-of-9 from the field in the Cavaliers' season opener in Bubbleville.

After posting a highly efficient 50–40–90 season under Tony Bennett at Virginia, Murphy declared for the 2021 NBA draft while maintaining his college eligibility.

[10] On June 21, 2021, Murphy announced that he signed with an agent, forgoing his remaining eligibility with Virginia and ending his collegiate career.

Murphy made his playoff debut on April 17, recording six points, four rebounds and two assists in a 110–99 Game 1 loss.

[18] In February 2023, Murphy was selected to participate in the Slam Dunk Contest at All Star Weekend in Salt Lake City, Utah.

[21] On October 3, 2024, the Pelicans announced that Murphy would miss the start of the regular season due to a right hamstring strain that he suffered during an evening practice at their training camp.