Starting from scratch may not fix the problem. What is the reason that is being given for the rejection? We may be able to assist you with resolving it. In some cases, the error cannot be resolved and you must print the return and file it by mail.
Once paid, there isn't a way to clear a return and start over but you could potentially start in another account, and request a refund for the duplicate return that you didn't use by contacting us here: Contact TurboTax.
Are you using the Online version or the Desktop program? You mentioned paying for state. Online has a fee for Federal too. Is just your state return rejecting?
Why is it rejecting? You should have received an email saying why or giving a reject code. If you can't fix it you will have to print and mail it.