A couple weeks ago I tried cutting a standard blank of Mother of Pearl for use as a musical instrument inlay. It was a complete failure.
Thought maybe a thinner material could work. So I tried a very thin 0.008" Mother of Pearl veneer. This is thin (and expensive) stuff, only about twice a thick as standard copy paper. You can see the difference between trying to cut the thick shell (right) vs. the thin MOP veneer on the left.
The latest cut is relatively precise with only slight discoloration on the edge and does not require a lot of power. So it could work where additional sanding (thinning) isn’t necessary. Keep in mind that because the material is translucent it is important that the inlay be placed within a solid colored backing, otherwise an unintended pattern might show through any finished work.
I believe it might still be possible to cut material in the 0.02" range with satisfactory results. That would be just thick enough to use for a fretboard application. Will try to get my hands on some.