In broad terms, I think you'd need to be programming in bare metal, which you can do on the Pi and would do anyway on a simpler ARM board. I think you'd need to act as an SPI slave, which is annoying because you won't get any hardware help. I suspect you'd have to react as fast as the host sends queries, which would mean no time to forward the inputs to a connected SD Card. Unless you forward by bit-banging to the connected card too!
The starting point then is to choose your ARM platform and find some bare metal tutorial. See if you can act as a dumb SPI peripheral first, perhaps: return a constant value, or a counter value. You'll almost certainly need to figure out how to drive your host as a general SPI master before moving up to using it to connect your emulated SD Card.
You might find some useful hints in the PiTubeDirect project, which acts as a bit-banged 8-bit peripheral on a 2MHz host bus.
https://github.com/hoglet67/PiTubeDirectI see some info about SD Card interfacing here:
http://elm-chan.org/docs/mmc/mmc_e.htmlAll that said, I'll defer to anyone who's actually tried to do some of this!