Initial indications are that AMD's Linux and open-source efforts will not be severely hit as AMD lets go of around 1400 employees worldwide.
AMD's John Bridgman has commented in our forums that they're still there. In particular, him and Alex Deucher along with their new open-source employees: Michel Dänzer, Tom Stellard, and Christian König. Even laying off one of these five open-source Linux graphics developers would be a significant (20%) hit.
At least for now it seems the open-source Radeon Linux developers are safe. Beyond providing hardware enablement of new Radeon hardware in the open-source Linux stack via code and documentation, there's added benefit to keep them around since AMD has ported the Linux driver to Windows (WEC7).
On the AMD Catalyst driver side as it pertains to the teams working specifically on the Linux bits, I haven't heard or seen (LinkedIn, emails suddenly bouncing, etc) of any pertinent people being let go there. Fortunately much of the code-base is also shared in the Catalyst driver between Windows and Linux.
The area taking the biggest hit is not in the AMD Graphics division but rather on the CPU ("AMD Legacy") side. It seems most of the slashes are occurring there since that's where AMD has been struggling as of late while their recent generations of graphics processors have been flourishing in popularity. Many have viewed AMD's recent launch of the first-generation CPUs Bulldozer architecture as being a flop and there are no immediate corrections insight.
Among the hardest hit at AMD with this downsizing is the press/marketing departments, where reportedly a majority of them were dismissed. It's hard to see any hard-working and dedicated individuals to be let go, but at least they didn't have much involvement with Linux. They really weren't familiar with the Linux topics, really not concerned about the Linux desktop enthusiasts, etc.
AMD's Linux engineers and other non-marketing folks tend to do a better job. Heck, AMD's John Bridgman alone has nearly 6,000 posts in the Phoronix Forums providing technical support, guidance, various bits of helpful information, and even cooking recipes. That's community/customer engagement!
In terms of any Linux / open-source engineers on the AMD CPU side losing their jobs, I have yet to hear of anything significant. I'm not nearly as well tapped with sources on the CPU side as I am with AMD Graphics, but so far there are no indications of any losses for developers that were working on new hardware support in the Linux kernel (e.g. Bulldozer patches), compiler optimiozations, or other matters. There might be a minor hit on their open-source / Linux work in Dresden, but so far that's unconfirmed.
If I hear anything else, expect a Phoronix update. There's already a second thread in the Phoronix Forums with users extensively discussing the lay-offs and AMD's future.