Raised in Hueytown, Alabama alongside his brothers Davey and his uncle Donnie, Clifford Allison grew up immersed in stock car racing. His brother Davey later stated that he believed Clifford was the more talented of the two younger Allisons, describing him as "crazy wild" — a combination of natural speed and fearlessness that defined his approach to racing. After marrying young, Clifford spent time working in a coal mine in Kentucky during the 1980s before returning to Alabama, divorcing, and eventually remarrying. He worked briefly as crew chief for his father Bobby's Busch Series team before that program was disbanded in 1988.
Allison began his professional racing career in earnest in the early 1990s. In 1990 he competed in the NASCAR Busch Series driving for Frank Cicci, attempting to win the Busch Series Rookie of the Year award, but was released by Cicci after the season's seventh race due to poor results. He drove on a limited schedule for Clint Folsom in 1991. By 1992 he had joined team owner Barry Owen with a plan to run the majority of the Busch Series calendar.
His best career result in professional stock car racing came in an ARCA race at Texas World Speedway in April 1992, where he finished second.
On August 13, 1992, during practice for the Detroit Gasket 200, a Busch Series event at Michigan International Speedway, Allison spun entering turn four and struck the concrete wall directly on the driver's side. Bobby Labonte and Richard Lasater were the first to reach him. He was transported to hospital, where he died shortly thereafter.
Investigators and officials offered conflicting accounts of the accident's cause. NASCAR vice president Les Richter maintained that the car's safety equipment remained largely intact and that the near-flush impact with the wall was simply a severe accident. However, witnesses — including an anonymous driver and crew chief whose accounts were published in The Atlanta Constitution on August 23 — stated that a broken seat had prevented the safety harness from functioning, allowing Allison to be thrown into the roll cage and sustain the fatal head injury.
In January 1996, Allison's estate filed a civil lawsuit against NASCAR, Michigan International Speedway, car-owner Barry Owen, helmet and harness manufacturer Simpson Performance Products, and seat builder Brian Butler. The presiding judge dismissed NASCAR, Penske Speedways (owner of the Michigan track), and Owen from the case. Simpson and Butler failed to respond to the lawsuit and were held financially responsible for Allison's death.
Clifford Allison was survived by his widow Elisa and three children: Brandon, Tanya, and Leslie. His death in August 1992 was the first in a devastating sequence for the Allison family: his brother Davey died in a helicopter crash at Talladega Superspeedway in July 1993, less than eleven months later. The two deaths within one year robbed NASCAR of the family's next generation and cast a long shadow over the Alabama Gang's legacy.