I don't know of a 'material' there is that you can use to 'practice' with before you go cutting granite but that's what I'd do especially if you're cutting, say, granite countertops. (It sounds like you're attempting this type of job for the 1st time.) It would be a costly mistake if you don't know enough about the 'process' (which I don't and you're asking ...) I'm sure someone can 'tell' you what it all involves but unless you can practice, or afford the mistakes, you may still not know enough of the 'little things' to get you 'through the granite' safely and correctly.
Obviously, you'll need a powerful saw (table or hand-held, depending on how big the pieces are that you're cutting), and diamond blades. You didn't ask but I'll say it anyway, ... I'd leave this part to a pro any day!