Why would you be able to?
Whoops. Sorry, I'm not an accountant. Check with an accountant.
If the other party was at fault, his/her insurance should pay for some of your losses. And if you were at fault, your insurance should. If the car was used for business, you may have some additional options. Again, check with your accountant.
But just because someone makes a mistake doesn't mean it's tax deductible.