The limiting factor in this type of device is the frequency at which the DSP engine runs. I believe that is 96 kHz for the miniDSP SHD series, so files at 192 kHz will be downsampled. I don't know how it handles DSD, but if it does DSP on them, they would need to be converted to PCM at the DSP frequency (96 kHz).
The DSP engine, of course, provides Dirac convolution, crossovers, and such.