Elliott was born in Tucson, Arizona as the youngest of three boys. He attended the G.A.T.E. (Gifted and Talented Education) program at Tolson Elementary School there, then played basketball at Cholla High School (now Cholla High Magnet School) on the city's west side.
After graduating in 1985, he remained in Tucson to play college basketball at the University of Arizona. Under the tutelage of Lute Olson, Elliott was selected as a consensus all-American during his junior and senior years, and led the Wildcats to the Final Four in his junior year (1988). Elliott broke Lew Alcindor's (Kareem Abdul-Jabbar) all time PAC 10 career scoring record. After an exceptional senior season, Elliott won the Wooden Award. He is still the University of Arizona's all-time leading scorer.
Elliott was drafted by the San Antonio Spurs in the first round of the 1989 NBA draft under Coach Larry Brown. The 1989-1990 season was also the first for Elliott's teammate David Robinson, who would play as the team's superstar. Elliot would go on to start in 69 of 81 games for the season, averaging 10 points a game, and the Spurs would make the playoffs where they would sweep the Denver Nuggets in the first round before falling to the eventual Western Conference Champion Portland Trail Blazers in 7 games. Elliott increased his scoring average to 12.7 during the postseason.
In the following season, Elliott started in all 82 games, increasing his scoring to 15.9 points a game, and the Spurs led by Robinson won 55 games, but lost in the first round of the playoffs to the Golden State Warriors in four games. Elliott once again increased his scoring output in the playoffs, and the Spurs looked forward to improving. The 1991-1992 season would be a tumultuous one for the team, with Brown stepping down as coach after a 21-17 start, replaced by Bob Bass. The Spurs still managed to win 47 games with Elliott starting in all 82 games and averaging 16.3 points, but San Antonio would go on to be swept in the first round by the Phoenix Suns. Like in his first two years, Elliott increased his scoring in the playoffs to 19.7 points a game for the three game series.
Coaching changes would once again destabilizing the Spurs' season, before John Lucas II took over the team, leading them to 55 wins on a 39-22 record after the team opened the season with a record of 10-11. Elliott played in 70 games, and once again placed second in scoring on the team to Robinson with 17.2 points a game, including a career-high 41 points against the Dallas Mavericks on December 18, 1992. He would also be named to play in the 1993 NBA All-Star Game along with Robinson. In the playoffs, San Antonio defeated Portland 3 games to 1, before facing the number one seeded Suns in the conference semifinal. After losing the first two games in Phoenix, the Spurs would respond with consecutive games at home, as Elliott scored 17 points in game 3 and 19 points in game 4. The Suns, led by superstar Charles Barkley managed to wrap up the series in the next two games. Elliot averaged 15.8 points per game in the playoffs.
Elliott spent the 1993–94 season with the Detroit Pistons after being traded in a multi-player deal which included Dennis Rodman. The Pistons had previously been a championship contending team, and were still led by veterans such as Isiah Thomas and Joe Dumars, but struggled throughout the season with injuries and failed to make the playoffs. Elliott started in 73 games, averaging 12.1 points a game. Following the end of the season, he would be traded back to San Antonio, who had lost in the first round in the 1994 playoffs.
Despite averaging a career high 18.1 points a game, Elliott was expected to be traded to the defending champion Houston Rockets in exchange for Robert Horry during the 1994-95 season, however the trade fell through when Elliott failed his physical. The Spurs were also now coached by Bob Hill, and would go on to win 62 games led by Elliott and Robinson, who won that year's NBA Most Valuable Player Award. The Spurs had clinched the top seed in the western conference, and would sweep the Denver Nuggets in the first round before facing the young Los Angeles Lakers in the semifinals. The Lakers pushed San Antonio to a 6th game in Los Angeles, where the Spurs won. Elliott scored 26 points, his high for the playoffs, in the series clinching game. The Spurs had reached the conference finals, where they would face Houston. Despite having home court advantage, the Spurs would lose the first two games at home, and would go on to win two games before falling to the more experienced Rockets in 6 games. Elliott averaged 17.3 points a game in the playoffs.
The 1995-1996 season would turn out to be a personal best for Elliott, as he averaged 20 points a game, a career high, in 77 games. Elliott also made a career high 161 three pointers on the season, and played in the 1996 NBA All-Star Game, scoring 13 points in 22 minutes. The Spurs once again came up short in the playoffs, defeating Phoenix in the first round before losing to the Utah Jazz in 6 games, with Elliott's scoring averaging falling to 15.5 points a game. The following season would prove a disaster for the Spurs, as Robinson played in only 6 games due to a season ending injury, while Elliott also suffered injuries that limited him to 39 games. The team would then be taken over by new coach Gregg Popovich, and their lottery status in the 1997 season led to the drafting of Tim Duncan in the NBA draft following the season. Injuries limited Elliott again to just 36 games in the 1997-1998 season, but the Spurs improved to 56 wins led by Duncan and Robinson, before losing to Utah in the conference semifinals.
Championship Season and Kidney disease: 1998-1999
The 1998-1999 season would be shortened to 50 games as a result of a league lockout, but the Spurs would win 37 of the games for the west's best record led by Duncan and Robinson, with Elliott starting in all 50 games with an average of 11.2 points a game. The Spurs entered the playoffs with a dominating defensive attack bolstered by the big man duo of Duncan and Robinson, and they first defeated the Minnesota Timberwolves 3-1 in the first round. San Antonio would then pull off a 4 game sweep of the much improved Los Angeles Lakers, led by superstars Shaquille O'Neal and Kobe Bryant. Next up would be the Portland Trail Blazers, another resurgent squad, in the conference finals. The Spurs would take game 1 on their home floor, and in game 2 the Trail Blazers held a 2 point lead with 9 seconds left to play in regulation. Elliott received a pass nearly stolen by Blazer Stacey Augmon in the corner, before Elliott caught the ball within an inch of the sideline (narrowly avoiding going out of bounds). He managed to stay on his tiptoes rather than planting his feet, before releasing a 21 foot three point attempt just over the outstretched arms of 6 foot 11 forward Rasheed Wallace. The shot went in, giving the Spurs a 1 point win and the eventual victory. The shot would go on to be called the "Memorial Day Miracle" because of its improbability and the date on which it was made. Elliott finished the game with 22 points. and shifted the momentum of the series to the Spurs, who would go on to sweep Portland. The Spurs had finally made the NBA Finals, facing the surprising New York Knicks, who had managed to make the Finals despite being the 8th seed in the Eastern Conference but who were missing star center Patrick Ewing. San Antonio dominated the Knicks in the first two games, and while the Knicks managed to win game 3, the Spurs combination of Duncan, Robinson and effective play by veterans such as Elliott (14 points in game 4), Avery Johnson and Jaren Jackson proved too much for the Knicks. The Spurs won game 5 in Madison Square Garden to wrap up the series and win their first NBA Championship. Elliott averaged 11.9 points in 17 games in the playoffs while shooting 40 percent from beyond the three point arc.
Shortly after the championship run, Elliott announced that he had played despite having a kidney disease, focal segmental glomerulosclerosis, and that he would require a transplant. He underwent surgery on August 16 of that year, receiving a kidney from his older brother, Noel. On March 13, 2000, Elliott became the first player to return after a kidney transplant, in a game against the Atlanta Hawks. He would only play in 19 games in the 2000 season, and San Antonio failed to repeat as champions. Elliott started in 34 of 52 games in the following 2000-2001 season, as the Spurs won the best record in the league but lost to the eventual champion Lakers in the conference finals.
Elliott announced his retirement in 2001. He finished his career averaging 14.2 points, 4.3 rebounds, and 2.6 assists per game. Elliott is the fifth all-time franchise leader in three-point field goals made (563) and fourth for three-point attempts (1,485).
After retiring, Elliott became a basketball analyst for The NBA on NBC and, during the 2003–2004 season, for ABC Sports and ESPN. He left that position for the 2004–2005 season and became the color commentator for the Spurs' local broadcasting. On January 5, 2013, he joined Fox Sports 1, calling his first college basketball game with the network.
On March 6, 2005, his #32 was retired by the San Antonio Spurs and was hung in the rafters of the AT&T Center. His #32 is also retired by the University of Arizona.