I need to clear and start over because Turbotax messed up my return but I've already paid. Is there any way to do this?

So you have already paid, but haven't yet filed anything?

It won't let you clear and start over if you already paid, but TurboTax Support may be willing to provide you the desktop software as a download.  Then you can start a new return.    You'll need to discuss it with them.

Here's how to reach TurboTax Support:

Hours are 5AM-9PM Pacific (8AM-12 Midnight Eastern) 7 days/week.

FAQ: What is the TurboTax phone number?
https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632

Or you can use this contact form to get a phone number, or it may schedule a call back.
https://support.turbotax.intuit.com/contact

If they do provide you the desktop software, be aware there is a 24.99 fee to efile a state return, except there is no fee for New York state.  And there is no fee to print and mail the state return.

If you already paid for a state return online, you could ask Support for a service code for the state efile fee, however, but I don't know if they will provide it.