Mitchell, a first round draft choice of the Cleveland Cavaliers in 1978, spent 10 seasons in the NBA, the final six-and-a-half of them with San Antonio.
He later played in Italy before retiring in 1999.
"At each stop in his distinguished career, he was a fan favorite thanks to his outstanding offensive skills and his humble, down-to-earth personality," Spurs coach Gregg Popovich said in a statement.
Mitchell, a forward, ranked among the NBA's top 10 scorers in four of his 10 seasons, averaging 19.8 points and 5.6 rebounds for his career.
He scored 14 points in 15 minutes in the 1981 All-Star game.
(Reporting by Gene Cherry in Raleigh; Editing by Mark Lamport-Stokes)