Haudenschild was born in Wooster, Ohio. He grew up watching his father John and later his brother Ed race modifieds and sprint cars, and began racing sprint cars himself at age 15 in 1974 at tracks near Wooster. His first sprint car win came in his second season, in 1975 at Lakeville Speedway.
Haudenschild scored his first non-wing sprint car win in 1981 at Lawrenceburg Speedway, driving for car owner Bob Hampshire. That same year, he won the Grand Annual Sprintcar Classic, the largest sprint car race in Australia, and returned to win it again in 1982. In 1982, driving for the Gambler house car owned by C. K. Spurlock and sponsored by Kenny Rogers, he won 30 A-main features.
His first major American win came in 1987 at the Kings Royal at Eldora Speedway, one of the most prestigious events on the sprint car calendar.
Much of Haudenschild's most celebrated work came during the 1990s driving for car owner Jack Elden in the famous Pennzoil No. 22. In 1993 he captured the inaugural Historical Big One at Eldora Speedway, a $100,000-to-win event. He won the Kings Royal two more times, in 1994 and 1998, in the Elden car. He also claimed Gold Cup wins at Silver Dollar Speedway in 1998 and 1999, and won the $50,000-to-win Front Row Challenge at Oskaloosa Speedway in 1999.
His best World of Outlaws points finish came in 1995 when he finished second — just 142 points behind champion Dave Blaney. He is one of only four drivers to have won both World of Outlaws and USAC races at Eldora Speedway.
In 2003, driving for car owner Larry Woodward, Haudenschild won the Mopar Million at Eldora Speedway. The race featured a million-dollar purse and required beating 138 other non-wing sprint car drivers across ten heats and six features; Haudenschild's payday was $200,000. It stands as the richest win of his career.
In 2008 he claimed his third Gold Cup win at Silver Dollar Speedway, the same season he recorded his 50th World of Outlaws win and his first career victory in Canada at Castrol Raceway.
Following the 2008 season, Haudenschild drove for a succession of car owners including Lon Carnahan, Dennis Roth, Paul Silva, Jamie Miller, Pete Grove, Gus Wasson, Richard Hoffman, and Tom and Sherry Leidig. He retired from driving in 2021 but continues to attend races as a spectator.
Haudenschild married Patty Sweeney in 1992. His son Sheldon Haudenschild has followed the family into sprint car racing, joining the World of Outlaws series full-time in 2017 and establishing himself as one of the top competitors of the next generation.
Haudenschild was inducted into the National Sprint Car Hall of Fame in 2009. His tally of 72 World of Outlaws wins places him 11th on the all-time list, and his victories in the Kings Royal (three times), the Grand Annual Sprintcar Classic (twice), the Historical Big One, the Gold Cup (three times), and the Mopar Million span four decades and multiple countries. His aggressive "Wild Child" style made him one of the most distinctive and popular figures in open-wheel dirt-track racing.