Murray was selected by the San Antonio Spurs in the first round of the 1992 NBA draft with the 18th overall selection. Just seven days after being drafted, on July 1, 1992 Murray was dealt twice in the same day. He was first traded to the Milwaukee Bucks for guard/forward Dale Ellis and then dealt by the Bucks to the Portland Trail Blazers for forward Alaa Abdelnaby. During the 93-94 season, he led the NBA in three point average at 45.9%. Murray spent two-and-a-half seasons with Portland before being dealt to the Houston Rockets on February 14, 1995, with guard Clyde Drexler in exchange for forward Otis Thorpe, the rights to Argentinian forward Marcelo Nicola and a 1995 first-round draft choice.