I am also facing this problem to cut SiC. I have 4H, 6H and 3C- SiC, 2'' and 4'' dia, 400 microns thick wafers. The way of cutting is by using ADT dicing machine with diamond wheel cutter. But still also I have some problem.
you can cut silicon carbide by grinding machine with diamond wheel cutter as i have cut. you can also use wire EDM but there are lot of things to care. you can see this article.
Chapter Experimental Study on Improving Material Removal Rate and Su...
Another option is using a waterjet laser. We can cut nearly any kind of freeform shape in Silicon Carbide and Boron Carbide. Thickness of 8mm we have done and depending on the size of the part to cut out it takes just a few minutes. You can see some examples here: http://www.avonisys.com/sic-silicon-carbide-laser-processing-cutting-drilling.html