Yeah, unfortunately, I'm still experiencing the occasional full-system beachball freeze with my Sapphire 7950 on Yosemite with the public beta. I've done what Arsen suggested but apparently I'm just unlucky. In fact, I grabbed a tiny 64GB SSD off the shelf and installed Mavericks just to make sure it's not the card going bad. No problems on 10.9.5, but 10.10.3 PB still has it. Last night I also wiped the main SSD that I had Yosemite on, installed 10.10.2 and didn't restore anything from Time Machine. Same issues, so I went ahead and restored. Reset PRAM earlier today. Same thing. I will say that the pauses are shorter in PB than they were in 10.10.2, though.
So in the public beta I used Feedback Assistant and learned how to do screen captures with Quicktime Player. I've taken video of the stutters, and the stutters are in the video. So Apple has some proof as to what happens.
edit: Wait. Arsen, are you saying you switched the BIOS switch to position 2 (PC mode)? So you don't get the boot screen, but the card works OK in OS X? That means for sure it's a BIOS/driver issue with the Hamachi personality that's used with the card in EFI mode. I'll try that out and report back.