a 10 year old with extremely bad behavior

Children do not pay attention unless there are consequences for bad behavior. Make her do chores to pay for the replacement tire (or for fixing it.) When she back talks, take 25 cents from her allowance (which she should get for doing basic chores). Or you can put a couple drops of hot sauce on her tongue. Expect her to be in bed at a certain time, lights off. If she doesn't go to sleep, that's her problem! Praise her when she does well. Talk with her teacher to find out if she acts this way at school. If she does, get professional counseling. If she doesn't, it's because she knows she can't get away with it there. Sometimes a real eye-opener is to stay a few days with another family (friend or relative) where the environment isn't as privileged as what she has at home. She doesn't appreciate what she has because she hasn't had to earn anything or show responsibility. Some consequences that I've found effective are: removing all TVs from the house for a week; going on "basic rations," which is making meals that are very basic (main dish, vegetable, bread, and milk); no sweets or desserts for a few days; taking away phone privileges; not getting to go on a family outing.

Have you spoken to her father about this? Have you brought her to counseling? Maybe there is something wrong that she does not want to talk to you about but will tell someone else.

What are you disciplinary tactics?

The biggest power a parent has is the childs allowance,my mother taught me from a young age,like the one time i kicked a hole in one of our houses doors,my mother deducted it from my allowance,I didnt have money for 3 months,believe it or not I never kicked a door in again.Personally I believe in a good hiding,but the allowance tactic is a very good alternative.

try sitting her down and talking to her if that dont work then take away her privilleges no tv grounded no friends or phone no allowance,if all else fails talk to school guidance.