Jimmy "Slice" Oliver attended Community College for one year and then transferred to Purdue University, located in West Lafayette, Indiana and played under head coach Gene Keady.

The 6'6", 208 lb guard-forward appeared in 31 games in his sophomore season, playing behind Center Steve Scheffler and alongside guard Matt Painter.

He helped lead the Boilers to a 2nd-place finish in the Big Ten Conference and to the Second Round of the NCAA Tournament with a 22–8 record.

Oliver was selected in the second round with the 39th pick by the Cleveland Cavaliers in the 1991 NBA draft.

After being invited to the Detroit Pistons' pre-season camp, he joined the CBA for the 1992–93 season, where he averaged 17.3 ppg in 15 games.