A demolition derby is supposed to be a kind of race in old beaten-up cars where it is allowed to smash into the other competitors. The more smash-ups the better. Usually the cars are reinforced by the owners in order to survive as many rammings as poss thereby staying in the race. Adding the word "kamikaze" gives the meaning a much more dangerous edge, and means that the competitors don't mind if they are killed. So, that's the scenario for a Kamikaze Demolition Derby. (This meaning is for the purposes of conveying a situation in a hopefully humourous manner, but of course no such type of race exists in reality.)
The definition in my neighborhood is as follows:
A Kamikaze Demolition Derby is what you inadvertently end up being part of when driving in Hounslow or Feltham in West London. This is in part due to the high concentration in the population of chavs
who drive around, high on whatever, in illegal cars. The can be spotted by the black or white smoke coming out of the back of the car, the colour red of the car, a head with a baseball cap in the driver's seat and acne on the very pale face, and if you get too close, will be cut up and then blamed for driving badly cuz you are a woman. You then see them drive off with squealing tyres smoking (they seem to love smoke of all kinds) and then nearly crash into the back of a bus.
Yes, it really did happen the other day. You know who you are wanker. Hopefully you will start another Kamikaze Demolition Derby soon which will cause you to be permanently removed from any future competions. Fuckwit.