Yeah, developed by Reflections, who made the Beast series, Brian the Lion and Awesome ..
I must admit that I never liked the arena stuff that much, I always prefer to do proper race.
Destruction Derby 1 is really fantastic. The graphics are rather weak (the game most of time has trouble to put the textures on the track properly), but the game is just fantastic. The tracks are perfectly designed, the control over your car is perfect, and the AI is probably the best I ever saw in a racing game (Each CPU driver has a different AI, you always see Learner Driver doing stupid things on track, while The Undertaker is always trying to hit other people in the track or The Passion Wagon doing always a fair race)