A diamond saw will definitely cut through any natural whetstone material. I wouldn't hesitate to pass a coticle through it (horrors!). I also cannot imagine why it shouldn't go through the Chinese 12K stones.
I still have a small one in the shop from the time I installed tile floors and it often serves admirably for chewing through bits of marble, Belgian blue stone, etc.
Do be advised that cutting speed is slow with a diamond saw and the noise of diamond blade on stone is not so pleasant to others in the area.
The only down side of this is the purchase price of the saw. It doesn't make economic sense for only a few cuts.