If I sign a Quit Claim Deed does that exclude me from personal liability if an accident occurs on the property and the property owner is sues?

If the accident occurs after you have relinquished ownership.

If I sign a Quit Claim Deed does that exclude me from personal liability if an accident occurs on the property and the property owner is sues?

If you don't own the property, someone is injured on it, and wants to sue, they probably aren't going to sue previous owners such as you. However I can conceive of situations in which they could allege that the condition of the property was your fault and claim that you are liable. So there is a remote possibility that you could still be sued.

If you believe there is a dangerous condition on the property, you should, in the agreement to sell, disclose it to the buyer, and the agreement should recite that the buyer assumes all liability, and agrees to hold you harmless, indemnify, and defend you from any such liability.