AMD has announced that they are launching a new ARM Cortex-A57 64bit ARMv8 Processor in 2014, targetted for the servers market.
ARM is getting hot lately, and they do compete with INTEL on server-side thus, it is not a bad strategy that AMD wants to jump in and ride the waves of ARM. If they have a good execution plan, they can make it work.
Designing their own cores does make sense for them - otherwise they do not have any differentiation. I doubt the one-size-fits-all cores from ARM can address all the markets. I would suspect that ARM's own cores would likely want to retain dominance in the mobile space and are targetted to those market first. This is not to say that they cannot be used in servers but a dedicated server design would compete better.
Based on the news coming out of the ARM camp, it seems to validate this - almost all of them - AppliedMicro, Cavium, Qualcomm, nVidia are indicating they have their own core designs.
AMD does have decades of experience designing CPUs so that is their strength - the question is that of execution and focus when trying to ride two horses at once.
AMD is unique in that in can do both x86 and AMD, but as analyst Nathan Brookwood pointed out to me over lunch today, there's no great advantage to that.
Also, Nathan said he thinks there's no great advantage to designing your own custom core either given ARM is doing a pretty good and timely job covering the waterfront with its own designs.
Nvidia Tegra folks say Qualcomm, for example, went to a lot of trouble to design its own ARM cores but is not getting a huge technical advantage with them.