David, my point in posting is that I don't believe the problem is specific to the Radeon 7950. My mini has a built-in Radeon 6630M. I've also seen a similar post for Radeon 5870. Based on all decriptions, I think it's the same root problem. The interesting difference here though is that this is built-in factory hardware, not an add-on card. And obviously, there's no "pc/mac switch".
I have talked with StarTech. They indicated that they have working minis, using the adapter. I didn't ask though if their mini's were using Radeon or Intel Graphics. This was an option on the mid-2011 mini.
You mention, pc vs mac mode and compare that to an incompatibility in the adaptor. Remember, that the adaptor is on the other end of the displayport. The thing that changed is the graphics driver inside the mini - the same Radeon driver that impacted your card.
Other notes: The adaptor is not dead, because it's successfully displaying the white screen and apple logo at boot. The monitor is fine for the same reason and also because my PC can drive it just fine. The display port functions because of the white logo. The display port also works with a VGA adapter (don't know that this tells us anything useful). The problem first manifested itself during the 10.9.2 patch process.
I've submitted an apple bug report. Apple hasn't responded, but the bug has been marked as a duplicate - so someone else has reported similar.