Despite never winning in the Cup Series, he was still a fan favorite in the series.

Mast grew up in racing as his father and uncle were both race team owners. He began racing at age 16 at Natural Bridge Speedway and Eastside Speedway, after he traded an Angus cow for his first car. After dominating at the hobby track level for the decade, Mast began running the Busch Series in 1982, and had four top-ten finishes in 11 eleven starts in his #22. Mast's first full-time season came in 1985, where he had fifteen top-ten finishes. Two years later, he would win his first NASCAR race at the Grand National 200, then followed it up with another win the next week. He finished 11th in points that year. He improved to eight positions in 1988 the same year he made his Winston Cup debut for Buddy Baker at the Busch 500, finishing 28th at that race. Mast won five races while running full-time the next two years, before focusing his efforts on Cup.

Mast ran 13 races for Mach 1 Racing in 1989, finishing sixth at the Daytona 500, which Mast called his proudest achievements in racing. Mast ran selected races in 1990 for D.K. Ulrich before finishing the year with Travis Carter Motorsports. In 1991, Mast signed to drive the #1 Skoal Classic Oldsmobile for Precision Products Racing. He had three top-tens and finished 21st in points. The next year, Mast won his first career Cup pole at the Hooters 500, but a first-lap crash kept him from challenging for the win. Mast had a career year in 1994, with ten top-ten finishes, finishing a career-best second at Rockingham Speedway, as well as winning the pole at the inaugural Brickyard 400, finishing eighteenth in points. 1995 was disappointing in comparison, with only three top-tens. Skoal left at the end of the season, and Hooters replaced them. He had three top-tens late in the year, but when the season came to a close, he and Hooters left PPR.

Mast signed to drive the #75 Remington Arms Ford for RahMoc Enterprises in 1997. An omen of what was to come appeared early as Mast failed to qualify for the Daytona 500, and rumors started about RahMoc co-owner Butch Mock firing Mast after the race. Those rumors were later proved to be unfounded, but the season was a struggle, and Mast finished 32nd in points that year. 1998, started off better as Mast won the pole at the GM Goodwrench Service Plus 400, but the struggles continued, and he left the team when the season came to a close.

After rumors spread that Mast would return to Travis Carter to drive a car sponsored by Kmart, he joined the #98 Cale Yarborough-owned team, despite the fact that the team did not have sponsorship. Midway through the season, the team got sponsorship from Universal Studios, and Mast posted two top-tens and became the first driver since Yarborough to go the whole season without failing to finish a race. Unfortunately, Universal did not renew their contract, and with questions surrounding Yarborough's plans on continuing to own the team, Mast was out of work again.

During the early part of 2000, Mast climbed on board to drive the #41 Big Daddy's BBQ Sauce Chevrolet Monte Carlo for Larry Hedrick Motorsports. But after the Food City 500, Mast departed for A.J. Foyt Racing, and had two top-ten finishes.

Mast began 2001 with Midwest Transit Racing, but due to sponsorship issues, they only ran part-time, and Mast soon left to drive the #27 Sauer Pontiac Grand Prix for Eel River Racing, but late in the season, the team closed down, and Mast was out of work once again. Fortunately, he was able to get a deal with Donlavey Racing with Sauer continuing to sponsor for 2002.

Not long into the year, Mast began feeling ill suddenly. He had lost weight and was forced to miss races to take medical tests to find out was wrong. It turned he had suffered carbon monoxide poisoning. The illness forced Mast to retire, and Mast hasn't been heard from much since his departure.