Can I write off my car, had liability and it was totaled by my kid driving it without my permission?

Sorry--no.   Casualty losses are not deductible on a federal tax return unless you were in a federal disaster area and the loss was caused by the disaster.   Talk to your child about paying you back.

Casualty losses for personal property are limited by current law. For tax years 2018 through 2025, if you are an individual, losses of personal-use property from fire, storm, shipwreck, other casualties, or theft are deductible only if the loss is attributable to a federally declared disaster (federal casualty loss). 

See FEMA's website to find out what disaster areas have been declared that produced the types of casualties allowable for personal-use property.

On a personal tax return, you could only potentially have a deductible loss If the vehicle was used in a Schedule C business. If your property is business or income-producing property, such as rental property, and is completely destroyed, then the amount of your loss is your adjusted basis minus any salvage value or insurance or other reimbursement you receive or expect to receive.

See here for more information from the IRS on this topic.