From what you have posted you will have a BIG mess if you try to do this yourself. You have stated that you are trying to cut a finised moulded cutout in a granite slab for an undermount sink. This means you will have to cut a very precise hole and then mould the edge of this hole with a router and then polish that edge. This will be a very involved process in the field. You can look at routers and bits for this purpose at places like www.masterwholesale.com. They also sell polishing kits/pads and abrasives for the subsequent steps. The router bit alone might cost 400-500 dollars. This process is normally done in a shop with a CNC router. This is not something you do with a hand held woodworking router or a grinder.
If I were you and I were really trying to pull this off on my own I would go for a square edge sink hole. You would need a diamond core bit to match your needed radius at the sink corners (square/rectangular sink), a diamond blade, and a polishing set. It will be a LOT of work and a LOT of mess and will probably result in a substandard result as compared to a shop doing it but that may be acceptable to you. You could punch holes at each corner with the core bit, cut to those holes with a diamond blade, then polish a day or two. The end result could be anything from a disaster to somewhat acceptable.
If the hole needs to be oval, round, or must have a routed edge, I would not even consider doing it.