No. You can't willfully damage their property for trespassing. You can remove it, but removing a car is not trivial. If you call a towing company, that's your dime.
In California, all you have to do is post a sign warning that unauthorized vehicles parked at that location will be towed at the car owner’s expense. As long as the sign includes the contact information for the towing company, then you are able to enforce.
Here is what the City of Mountain View states on their Police Department web page:
Business and apartment owners may restrict parking on private property to employees, customers or residents. Cars can be towed from private parking areas only if tow-away zone signs are posted at each entrance to the parking lot.
Often property owners hire a tow company. Owners may authorize the firm to tow violators without a request from the business. This means tow companies may drive by, at any time, to spot violators and collect tow income. Otherwise, property owners must initiate a tow. In either case, your car might disappear without warning, at your expense, if you violate posted signs on private property.
Mrs. Flash just recently did or didn’t park across someone’s driveway. She swears she didn’t and thinks someone pushed the car up the block, which I find difficult to believe. Anyway the cops ticketed it and had it towed, and I had to go take care of it. I guarantee you, none of it was on the homeowner’s dime.