Cooper was born in Los Angeles. When he was three years old, he cut one of his knees severely, requiring 100 stitches to close. At the time the doctor said that he would never be able to walk. He attended Pasadena City College before transferring to the University of New Mexico. He played for the New Mexico Lobos for two seasons, 1976–78, and was named first team All-Western Athletic Conference. In his senior season the Lobos won the WAC title, with Cooper averaging 16.3 points, 5.7 rebounds and 4.2 assists per game.
Selected by the Los Angeles Lakers in the third round of the 1978 NBA draft with the 60th overall pick, Cooper became an integral part of their Showtime teams of the 1980s with his defensive skills. In a twelve-year career, he was named to eight NBA All Defensive Teams, including five First Teams. He won the NBA Defensive Player of the Year Award in 1987. He, along with Kareem Abdul-Jabbar and Magic Johnson, was a member of five Lakers championship teams in 1980, 1982, 1985, 1987 and 1988.
At 6 ft 5 in (1.96 m), 174 lb (77 kg), the rail-thin Cooper known for his knee-high socks, played shooting guard, small forward, and point guard, although his defensive assignment was usually the other team's best shooter at the 2 or 3 position. Larry Bird has said that Cooper was the best defender he faced. For his career, Cooper averaged 8.9 points, 4.2 assists, 3.2 rebounds, 1.2 steals, and 0.6 blocks per game. A popular player among Lakers fans, home crowds were known to chant, "Coooooooop" whenever he controlled the ball, and the Lakers sometimes ran an alley-oop play for him that was dubbed the "Coop-a-loop." Leaving the team after the 1989–90 season, he was ranked among the club's all-time top 10 in three-point field goals (428), games played (873), total minutes played (23,635), steals (1033), blocked shots (523), assists (3,666), defensive rebounds (2,028), offensive rebounds (741) and free throw percentage (.833).
He then played for the 1990–91 season in Italy for Pallacanestro Virtus Roma in the Italian Serie A, averaging 15.8 points, 6.1 rebounds, 1.9 steals, 1.8 assists, and 0.3 blocks per game.
Following his playing career, he served as Special Assistant to Lakers' general manager Jerry West for three years before joining the Lakers' coaching staff in March 1994 under Magic Johnson, then with Del Harris from 1994–97. He became an assistant coach of the WNBA's Los Angeles Sparks in 1999, and helped the team reach the playoffs for the first time in franchise history, with a record of 20-12.
He was named the Sparks' head coach in November 1999, and the Sparks' record quickly improved, as they finished 28-4 in their 2000 campaign. Cooper was named the WNBA Coach of the Year for his efforts. The Sparks followed with consecutive WNBA Championships in 2001 and 2002, but were denied a third straight WNBA title by losing to the Detroit Shock in 2003.
After the Sacramento Monarchs ended the Sparks' run in the first round of the 2004 WNBA Playoffs, Cooper took a job as an assistant coach under Jeff Bzdelik with the Denver Nuggets. After 24 games, Bzedlik was fired, and Cooper was named the Nuggets' interim head coach. He remained interim head coach until George Karl was brought in to coach the team about a month later and served as a scout for the Nuggets the remainder of the season.
Cooper was the head coach for the Albuquerque Thunderbirds for two years (2006–2007). In 2007, Cooper left the Thunderbirds after coaching them to the National Basketball Association Development League Championship in 2006. Cooper then returned to coaching in the WNBA as the head coach of the Los Angeles Sparks.
In May 2009, Cooper was named the head coach for the University of Southern California's Women of Troy Basketball Team. He quit in 2013 after USC went 11–20 and finished seventh in the Pac-12 Conference with a 7–11 record. He was 72–57 overall at USC.
In November 2013, Cooper was hired by the Atlanta Dream as head coach.
In July 2014, Cooper was diagnosed with early stage tongue cancer. Cooper will have surgery at Winship Cancer Institute of Emory University in Atlanta, and a full recovery is expected. He was fired by Atlanta after an 11–22 season in 2017.