A possible reason why those Intel® Xeon® Processors don’t list the MMX and SSE instructions sets as supported is the fact that they are not intended to be used for multimedia operations like digital signal processing (DSP) and graphics processing, as a matter of fact they don’t have an onboard graphics controller. It is expected to use server or workstation boards with embedded graphics controller taking care of this type of operations.
In the other hand, most of Intel® Desktop processors support these instruction sets because they process multimedia operations like audio and video streaming.
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Checked some other materials with regard to AVX.
What I understood from these is that AVX complement older SIMD instruction sets (SSE) and can process eight single precision floating point numbers or four double precision floating point numbers, simultaneously compared to four single precision float point numbers or two double precision floating point numbers in SSE, inter alia!
Besides the increase in size, AVX also provides an extended i nstruction format which allows three input arguments in contrast to two input arguments all owed for SSE.
and so on...
To your point that "they are not intended to be used for multimedia operations like digital signal processing (DSP) and graphics processing, as a matter of fact they don’t have an onboard graphics controller."
Intel Xeon E3-1275v3 has built in Graphic processor (http://ark.intel.com/products/75464) and shows SSE4.2 and AVX support.
Useful links with regard to understanding SSE vs AVX:
So AVX does the same thing as SSE but more precisely with bigger data 256bit (SSE - 128bits).
The information you are providing is correct, AVX does the same as SSE instructions sets but using bigger data.
Xeon processors are capable to manage these instructions sets, however they were no meant to be used for multimedia purposes, but once you installed a graphics card, you will be able to use them.