Would this http://www.newegg.com/Product/Product.aspx?Item=N82E168... model of the GTX 670 fit in the Define Mini? I already know it will fit with the upper HDD cage removed, but would it fit even with the cage installed? Both the specifications listed on NewEgg and Fractals site state the maximum GPU length supported is 260mm with the cage installed, which comes out to about 10.2" if I remember correctly. I'm assuming it will fit, maybe without a lot of room to spare, but fit nonetheless.
Do not know alot a Nvidia anymore but from what I could see on Newegg most of the GTX 670 should fit within the 10.2 space. I would think you should be OK as long as you have a good PSU installed in that Mini. I guess the only thing I would be worried about would be adequate air flow in that case with such a large GPU.
I had a SeaSonic in mind for the power supply and the Define Mini can be optimized quite effectively to keep even a high-end gaming rig very cool. On the topic at hand though, I recently discovered a post over on HardForum where somebody was able to squeeze two Radeon HD 7970 cards into the Mini, which I believe are about 11" each, and the only modifications necessary was a slight notch to the top of the lower HDD cage so that the bottom card would slide in.