Drafted by the Cincinnati Reds in the 2nd round of the MLB amateur draft, Oliver would make his Major League Baseball debut with the Cincinnati Reds on July 15, , and appear in his final game on October 6, . Oliver was a member of the Cincinnati Reds team that defeated the Oakland Athletics in the 1990 World Series. Joe drove in Billy Bates from second base in Game 2 of the 1990 World Series with a hit off Dennis Eckersley to win the game and propel the Reds to the 1990 title. He now resides in Orlando, Florida and coaches a high school varsity baseball team at Pine Castle Christian Academy. He and his wife Kim have 4 children; Dejai, Karrah, Gavin, and Lauryl.