It will depend upon your state laws however in many states in order for a minor teen to obtain a permit and start the driver's licensing process you as a parent signed the application stating that you are responsible for the child as a driver.

If your state required a parent or guardian to sign a document or give consent in a different way in which to obtain an instruction or learner's driving permit then normally the parent or guardian can contact the Department of Motor Vehicles to revoke their minor child's driving privileges so the child would need to start the licensing process again at a later date.

Your local DMV should be able to give you information on if this is possible.

As for insurance, some insurance companies do not require your child to be added when they have a learner's permit but will allow you to wait until the child is fully licensed. Before revoking your son's permit you may want to check with your agent to see when your insurance provider would require him to be added to the policy.

If the licensing process to get a full license takes awhile then your son may not need to be added for awhile, again this can differ from one insurance company to another so check with your carrier and perhaps also shop around for cheap student car insurance.