Vandalism is covered under the comprehensive portion of an auto insurance policy. Physical damage coverages of collision and comprehensive both come with deductible amounts, which you choose at the start of your policy. So yes, you will have to pay the deductible associated with your comprehensive coverage when you have the damages caused by the vandalism repaired. In some states, there is an option of a deductible as low as $0 or $50 for comprehensive.
A homeowner policy usually does not cover your motor vehicle in an incident such as this, even if the car was vandalized in your own driveway. If your car was broken into and personal items were stolen out of it then a homeowner's or renter's policy will sometimes cover the items taken. It would depend upon the terms of your homeowner's policy.