Can you return a car after you sign the papers if the dealer says he made a mistake and can't give it to you for the price you signed for?

The question is a bit confusing.

When purchasing a car from a dealership, the transaction is by contract. Once the contract is signed, the contracted price is the price. There is no changing of minds later.

If, as is not unusual, the dealer sent you with the vehicle to return at a later date to sign the contract, and then changed the price, this could be an attempt at fraud. Get the change in writing, do not sign anything, and take your evidence directly to an attorney who specializes in consumer fraud.