I have signed a purchase agreement on a new build and the appraisal has been denied, the mortgage closing can't proceed, do I have the legal right to back out of the deal entirely and if yes, how do I do that?

I don;t understand the appraisal has been denied? Do you mean it came in lower that expected? Regardless, a properly written purchase agreement will always have a clause stating that if the home doesn't appraise out, that you can back out... Talk to your Realtor.

If the appraisal comes in less that the purchase price, the seller can reduce the purchase price. If not you have to right to opt out of the contract. As Joe stated talk with your Realtor.

Read your purchase contract carefully.

I'm not sure what you mean by "Appraisal Denied".. If the home did not appraise for the full purchase price, then it's up to the seller / builder to prove the value to the appraiser.. if your purchase contract states the sale is subject to appraised value, then you should have our out right there.. but understand some builders have added disclosures that state you agree to purchase the home even if the appraised value is lower than the sale price.. you should read your contact carefully.. .. I'm a Broker here in Scottsdale AZ and I only lend in Arizona. If you or someone you know is looking for financing options, feel free to contact me or pass along my information. 480-287-5714 WilliamAcres.com