You need to prepare two separate tax returns. The federal can be married-joint. Then, prepare an entirely separate return for New York for your spouse, filing as married separate. You can e-file the federal return but will have to mail in the New York return, as you can't e-file it if you don't e-file the federal return it was created from.
You are allowed to mail your New York return in since your spouse is a non-resident.
You could purchase the TurboTax desktop product that will allow you to prepare two returns for the same price. If you do that, you can transfer your online tax file to your computer so you don't need to re-enter everything.
You can do this by using the Tax Tools menu option on your left menu bar in TurboTax, then Tools, then Save your return to your computer.
Here is a link to allow you to purchase the desktop TurboTax product:
TurboTax Download Products
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