Elliott played high school basketball at Cholla High School in Tucson, and played college basketball at the University of Arizona, under the tutelage of Lute Olson, and won the Wooden Award after an exceptional senior season. He was drafted by the San Antonio Spurs in the first round in 1989. Elliott spent the majority of his career with the Spurs, with the exception of the 1993-94 season, during which he played for the Detroit Pistons. Elliott was an instrumental part of the Spurs' successful NBA title quest in 1999: he tight-roped the right sideline and launched a three-point basket to edge the Portland Trail Blazers in Game 2 of the Western Conference Finals. This play, referred to as the "Memorial Day Miracle", shifted the momentum of the series to the Spurs.