My PhD supervisor cannot promise me a date to defend my dissertation before my visa expires. Should I just quit my PhD and start over? I am doing my PhD in Germany and I’m under a three year DFG grant, which ends in September, and with it my visa. Although I can get an 18-month visa to find a job after my PhD, this won’t be granted until after my defense (when I get my certificate).

My supervisor had no idea that my residence in Germany depends on my employment contract/grant with the university. 
I asked him if I could submit my dissertation at the end of July and be guaranteed a defense date in September. He told me cannot guarantee this and that I’ll just have to submit my defense earlier.

I don’t want to rush my writing (I’m technically submitting my PhD early already) so finishing earlier than July is out of the question. But if I don’t get a defense date in September, I will have to leave Germany and come back to defend it. I come from a country that requires a Schengen visa, so coming back won’t be as easy as hopping on a plane. 

Right now I am seriously considering submitting my thesis in July and then flying back at the end of September with or without a defense date.  If I don’t get a defense date then I effectively quit my PhD.

What should I do? Any advice would be appreciated.

EDIT 1: Thanks for all of your advice. I'm slowly going through it.

I asked my supervisor if I can do it remotely and he said that Skype-ing for dissertation panels is not allowed. So he won't even consider a virtual presentation.

EDIT 2: My supervisor and I had a meeting and we discussed a few options. Since we are inviting a professor in the US to the panel, it is in everyone's best interest to have a tough timeline in mind. The timeline we selected is within the validity period of my current permit. Still no guarantees as anything could go wrong, but it's better than nothing.

Thanks again for those of you who gave thoughtful responses. To those of you who thought my question "makes no sense", I apologize deeply for my profound ignorance and I'm sorry that you didn't find my question relevant, unlike many people here. (Ironically my thesis is about online communities and how some more established members treat less active ones.)
You should talk immediately with the International Office (or equivalent) at your university, as well as any student-coordinated offices at your university. This is by no means the first time that they will have dealt with such a situation. Usually there are workarounds available—for instance, you could be extended on a part-time contract for a few months while waiting for the defense to be completed. You certainly do not need to be employed full-time to qualify for a visa—you just have to be able to show sufficient income, which even a 50% contract would be enough to satisfy. 

However, I should point out that, depending on the university, there is no way to guarantee that you can turn in your thesis in July and be able to defend it in September. For instance, in the faculty where I used to work, reviewers were given three months to review a thesis. So if you turned in your thesis in July, you probably would not be able to have a defense before the beginning of November. You'll need to check the regulations for your program to see when the defense can be scheduled relative to the thesis being handed in.

Moreover, the "art" of scheduling a thesis defense requires getting enough examiners together at the same time, never an easy task in the German system.

However, to answer your main question, don't you think that quitting and starting over is counterproductive? If you're already writing a thesis, that shows you're relatively near to completion, and that your advisor thinks you're ready to move on. Giving that up because of the logistics of scheduling a PhD defense seems very shortsighted. Why would you not think that the same thing couldn't happen if you started over and worked somewhere else? Since you're so close to finishing, get it done!