How can I Access Tiger Sharc DSP processor through host pc?
If the user wants to boot the DSP as well as communicate with it, then the TigerSharc has got LinkPorts (tm), which can be used for both high speed communication, and booting.

The question is, how to connect to those to the PC. The PC doesn't have linkports, the DSP doesn't have PXIe. The obvious answer is to put whatever glue logic that's needed into the FPGA. 

Presumably you have already sorted out a PC to FPGA solution? I'd be using PXIe for that, fast, universal, supported with hardware both ends and by stacks of software, long history of use. That, or ethernet, same list of benefits, but with a different flavour.

Now your task is to design an interface and API that sits in the FPGA and exposes the DSP facilities, without feeling like an FPGA to use, but instead feeling like the DSP's peripheral devices. Perhaps a bit-bang register to control any mode pins, and some dual port memory to put the boot code into. 

High speed comms will depend on what the DSP is running, an RTOS, or something closer to the metal? Ideally Analog will provide drivers to make its link ports look like TCP/IP or PXIe to talk high speed comms with the PC, and you'll simply put a hub or bridge in the FPGA. If not, then you're designing a special interface.