I tried it when I first started making calls. Here's a few pointers if you feel you have to use it for a pot call...
Cut it outside with plenty of air circulation. Slate creates a very fine dust that will stick with you if you breathe it.
You can buy a tile cutting blade for a jigsaw (scroll saw) that will cut it fairly clean.
You will likely need to split it to get a thickness that is usable. This can be done with a fine chisel (made for stone, not wood) or even a stiff putty knife, etc.
As crazy as it sounds, you can make rough cuts on slate with heavy tin snips.
When it comes down to it, there is no way you are going to get as clean of a product as you will from Penn Big Bed Slate for about $1.50 a pop. There is no way I would go back and try to cut my own again.