A native of Inglewood, California, Miner first came to prominence as a high school player. A stand-out on his team at Inglewood High School, Miner's spectacular dunking ability resulted in his being given the nickname "Baby Jordan", in reference to fellow NBA high flyer Michael Jordan.
Miner attended USC from 1989 until 1992. As a junior in what would be his final season with the team, Miner's play earned him Sports Illustrated magazine's selection as the college basketball player of the year over such notable candidates as Shaquille O'Neal and Alonzo Mourning. Miner led the USC Trojans men's basketball team to a #2 seeding in the 1992 NCAA Men's Division I Basketball Tournament. The Trojans were upset in the second round, however, falling on one of the most famous baskets in the tournament's history — a three-pointer at the buzzer by James Forrest of Georgia Tech.
Miner left college after the 1992 season and declared himself eligible for the 1992 NBA Draft. He was selected by the Miami Heat with the draft's 12th overall pick.
Miner won the NBA Slam Dunk Contest twice, in 1993 and 1995. In the 1995 contest, Miner defeated Isaiah Rider, who had won the previous year, solidifying Miner as one of the game's best dunkers. However, his playing career proved unremarkable and failed to live up to the high expectations with which it began. Despite his dunking prowess, Miner did not get much playing time from Heat coaches, Kevin Loughery and Alvin Gentry.
I always felt the worst thing to happen to Harold was the "Baby Jordan" tag.
— George Raveling, Miner's head coach at USC
After the 1995 season, Miner was traded to the Cleveland Cavaliers. He averaged only 3.2 points and 7.2 minutes per game for the Cavaliers. On October 18, 1995 he was traded to the Toronto Raptors for Victor Alexander, but that trade was rescinded 4 days later when Alexander failed his physical. Miner played five scoreless minutes in his last NBA game, a 26-point loss to the Chicago Bulls on February 20, 1996. Cleveland waived Miner, having played him in only 19 games that season. He tried out for the Toronto Raptors the following year but was cut during the preseason. Rather than continue to pursue a career in professional basketball, either in the NBA or overseas, Miner retired from the sport.
As of early 2007, Miner had settled near Las Vegas, Nevada and was reportedly an active real estate investor. He was married and had one daughter. Since his retirement from basketball, he had been disinclined to give interviews or make public appearances, instead remaining private and largely inaccessible.