Spencer was an all-state basketball player at Eastern High School in Middletown, Kentucky (now part of Louisville); as both a junior and a senior, he led the team to the KHSAA state tournament in Lexington.

That season Spencer paced the Cardinals in scoring (14.9 ppg), rebounding (8.5 rpg), blocked shots (69), and field goal percentage (68.1%).

As a rookie, Spencer split time at center with 7-foot-3-inch (2.21 m) veteran Randy Breuer, but still managed respectable numbers, averaging 7.1 points and 7.9 rebounds per game, and shooting 51.2% from the floor.

[1] Additionally, he blocked 121 shots, establishing a single-season record for the young franchise that would stand until Kevin Garnett's rookie season in 1995–96.

In Utah, Spencer became the successor to Mark Eaton, and he provided the Jazz with solid scoring, rebounding and defense at the pivot position.

His role was diminished in 1997–98 by the arrival of second-year man Erick Dampier as the starter, as well as the drafting of rookie Adonal Foyle, and he saw relatively limited action as a reserve in 68 games.