You should be able to remove or modify the grips.
Loosen the bolt, and see if the grips turn. The grips may be attached to your grip shifter, although they are usually two distinct parts.
I don't deal with MTB bikes much, but I'd imagine that there is some kind of compression joint inside the grips to help keep them from twisting (helpful with the ergonomic style grips).
Looking at the part, likely a simple rubber compression, although there could be a compression joint like you have on your mirror.
Similar to bar end plugs?
"Ergon" brand grips are the biggest ergo grip brand. It appears as if they are locking (external band), and have a removable plug for your mirror.
Produkte ? ERGON BIKE
Nonetheless, I think you could force your mirror to work,