A stone cutting diamond coring bit is required to cut the granite. The procedure is to use correct RPM, pressure and keep bit cool as possible. A sponge and a bucket of water works quite well for cooling. Surprisingly, it cuts relatively fast. The problem is that the bits can start at $75 and up. Search the net - granite core bits - for product info and speed specifications.
As to the mounting hole, start with a small 1/8" stone / masonry drill bit with a hammer drill and use water to keep the hole clean and the bit cool. Finish with a larger size bit for the bolts. Take your time.
Scott Zuhse, Instructor
Micro Matic Dispense Institute