Mac Pro 3.1 with GTX 770 won't boot
There are no drivers for NVidia 3rd party cards in Mojave.
Support ended at High Sierra.

MacVidCards - Which driver should I install for my new GPU?​ is pretty much the authority on this topic. 

You can get to Mojave if you have a supported* ATI/AMD GPU with Metal capability, otherwise stay on High Sierra.

*Recommended GPU list, again from MacVidCards - I want the best graphics card for my Mac Pro, where do I start? No 3rd party drivers are needed for AMD cards, they still have Apple support - but only to Mojave, no further, for Mac Pro 3rd party cards.