Beauchamp began after WW2 racing old model stock cars at local county fair tracks and in 1949 he, teaming up with mechanic Dale Swanson, had a number of wins racing hotrods in Iowa, Nebraska, and elsewhere. He raced unmodified old model stock cars at Playland Park track in Council Bluffs, Iowa, finishing second in season points behind Tiny Lund. In 1951 Beauchamp won five straight features at the Playland track and was season champion. In 1954 he once again was season champion at the Playland track. He began occasionally racing late Models in 1953, and in 1955 Beauchamp began in midseason racing in IMCA, International Motor Contest Association. At the time the IMCA was one of the major racing associations in the midwest and a counterpart to the southeastern NASCAR racing organization. In 1956 driving a Dale Swanson owned Chevrolet, Beauchamp won an unprecedented 38 IMCA races while Chevrolet's won approximately five races in the NASCAR racing association. He repeated as season IMCA champion in 1957, winning the award for top stock car driver of the 1957 season. In 957 mechanic Dale Swanson was hired by Chevrolet to help build race cars at its semi-secret shop, SEDCO, in Atlanta, for the 1957 February Daytona Beach race. Beauchamp finished second in the beach race, and was the only car on the same lap as winner, Cotton Owens.
Beauchamp and his owner mechanic Roy Burdick were certain they really won the first Daytona 500 and their belief had nothing to do with the photo finish. Instead, they believed Lee Petty was one or two laps behind. The Petty pit was close to the Beauchamp pit and the Burdick crew believed Petty had made several more pit stops than Beauchamp. Petty, as Beauchamp and Burdick learned, had somewhat of a pattern of winning races when drivers and officials believed he was a lap behind: Concord 1958, Daytona 1959, Atlanta 1959, and Weaverville, 1960. Burdick and Beauchamp believed NASCAR had a lap counting (known as scoring) Problem, and part of the Problem was NASCAR had the drivers' wives counting the laps.
In 1959 another excellent mechanic from Playland and IMCA competition, Roy Burdick, an Omaha mechanic, was offered by Holman-Moody, a well-known center of Ford racing, to buy a Thunderbird for 5500 dollars to enter in the first Daytona 500. Burdick agreed and asked Beauchamp to drive the car. Beauchamp found himself leading the race when Fireball Roberts went out on lap 43. For the remainder of the race, Beauchamp raced near the front, usually in first,second, or third. On lap 149, Lee Petty who had been too far back in the pack to be noticed, suddenly appeared driving side by side with Beauchamp. For the last fifty laps the two continued racing close together. Beauchamp crossed the finish line at about the same time as Lee Petty in the Daytona 500 in 1959. Beauchamp was declared the unofficial winner of the race, so he drove the Roy Burdick owned car to victory lane. Petty protested the win. "I had him by two feet," Beauchamp said. "I glanced over to Lee Petty's car as I crossed the finish line and I could see his headlight slightly back of my car. It was so close I didn't know how they would call it, but I thought I won." NASCAR founder Bill France, Sr. studied photographs and newsreels for three days before declaring Petty the official winner. Beauchamp competed in seven events that season; recording his first NASCAR victory at Atlanta's Lakewood speedway where he lapped the entire field of NASCAR drivers. Although he had several high finishes in 1959, his final points of the season are not listed in the record books.
In 1960, he raced for Holman Moody and Dale Swanson in eleven events. He won his second and final NASCAR race that year in a 400-mile event at Nashville Speedway USA. Beauchamp and Petty were involved in an accident at the 1961 Daytona 500 Qualifier #2. Leader Banjo Matthews lost control of his car, spinning in front of the field. Petty and Beauchamp's cars sailed out of turn four and landed outside of the racetrack. It also was Beauchamp's last NASCAR race; though he only suffered head and back injuries.
In 1966, Beauchamp was the track champion in Peoria, Illinois.
