I have to throw my hat in the ring, as well. Same problem as everyone else. I have 2 EVGA Geforce 970 GTX cards in SLI. My crash is a black screen with sound but after that the PC locks up (in black screen not BSOD).
I have this EXACT same problem with Far Cry 3. I found a workaround in FC3 which was to turn the settings down using the preset video packages (low/med/high/ultra). The preset that worked for me was medium. As I started dialing individual settings from there, things went bad in a hurry.
So I get the same behavior from Witcher III that most of you are saying, the very first rendered cut scene crashes after 1-2 minutes if even that. I didn't have time to play with it last night but this is exactly what I'm seeing and dealing with in FC3.
I tried everything in FC3 to fix the problem - reinstalled drivers, turned up the card voltage, turned off SLI and ran single card, switched to DX9, etc etc. But the only thing that worked was turning the settings down to medium. I monitored card temperatures and ran the game for a while until I knew it would crash, then tabbed out to see the card temps, they were 68C and 75C - nothing really too out of bounds.
The other thing I noticed was that Far Cry 3 always seemed to crash when it hit a loadpoint or checkpoint of some sort - or even some sort of game boundry that triggered a radio sequence or something.
Seeing this thread makes me seriously wonder if there's not a fundamental architecture problem with the 970s. From what I remember the 970 architecture is different than the 960, not just expanded or enhanced.
Tonight I will try turning settings down and see if that helps, but its off to work, now. Very frustrating.
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Oh one more data point on my same problem with FC3. A workmate told me to try using the GeForce Experience and let that application dial in your optimized settings. I did this last week before I went on vacation, and the game ran well all weekend. It was a little choppy which was frustrating but it never crashed. Unfortunateley, as I tried playing Witcher III yesterday, and found the same black screen crash as in FC3, I opened the GeForce Experience thinking I'd let that application optimize for me. So I tried that and still got the crash. It was then I figured out that I didn't even have SLI on anymore, so my Far Cry 3 success might have been just a mirage (not it makes sense why it was so choppy).
So now I have to go see if FC3 actually is fixed with the GeForce experience optimization or if that only worked with one card enabled.
I know this post may be useless to some but hopefully I can inspire another train of thought in someone who might solve the problem for all of us.
One last thing - when I turned SLI back on my cards and tried optimization in the GeForce Experience, all of a sudden none of my games would optimize. So I found out that a lot of others were having the same problem. I inadvertently found a fix for that (I think) by tabbing over to drivers and having it search for updates. It came back saying no updates were available, that I was up to date. THEN I was able to optimize the games. Still didn't help with the Witcher, but might work for some of you.