There are a lot of missing facts here, so I can't give you a definitive answer. You said you're an independent contractor but that you have an employer. Do you have a contract with the car lot? That's where I would look first for questions regarding liability for things like fender benders. You use the word "garnishment," which implies that there has been a court judgment. Is that the case, or is the car lot just docking money you have earned? The law disfavors such self-help remedies unless it is in the contract language. Also, are you really an independent contractor? The IRS is wary of situations where employers call their employees "independent contractors" just to avoid the tax implications.
You should see if an attorney in your area would offer a free consultation so that questions like this can be answered and you could get a specific answer. If I've read the facts in your question correctly, you also should be prepared to leave this employment situation.
This answer is for informational purposes only, and it not intended to create an attorney-client relationship. I've had only the limited amount of information provided in the question from which to form an answer. Your best course of action is to set up a formal consultation with a qualified attorney in your area.
Generally, wages cannot be garnished without a court order. Garnishment involves a third-party trying to get your money - such as the IRS for taxes owed, child support, defaulted student loans. But this doesn't sound like "garnishment." Rather, it sounds like your employer is merely docking your pay for damage you caused while on the job. That, I'm afraid, is legal - unfair to a hard-working young person, but legal. Your employer should have had the damage paid by its insuranance carrier, rather than sticking you with the bill.