The only film I can recall like that isn't a horror movie:
Grandview, U.S.A. (1984)
starring C. Thomas Howell, Jamie Lee Curtis, Patrick Swayze, Troy Donahue, Jennifer Jason Leigh, William Windom, M. Emmet Walsh, John Cusack, Joan Cusack
Life in the small town of Grandview, Illinois is one that is just like any other city or town. Tim Pearson, soon to be graduating high school wants to go to Florida to study oceanography. He meets Michelle "Mike" Cody and is attracted to her. She runs the local Demolition Derby place. Ernie "Slam" Webster is one of the drivers in the derby whose wife is cheating on him and wants to later on be with Mike. Tim falls for Mike and a big love triangle is about to happen.
C. Thomas Howell and Patrick Swayze also costar in "The Outsiders" and "Red Dawn".
Otherwise, I can't think of any other film that involves a demo derby. I'll check around some more.