Will you be working underneath the counter or can you turn it over?
I think you should determine the adhesive used before you go much further. Buy some cheap woodworking chisels and sacrifice them to scrape off some globs of adhesive that might have oozed out from between the sink and the granite. Them test them with heat and various nasty chemicals (e.g., Acetone, MEK) to see if they respond to anything.
If something like MEK does soften the stuff, then build a little putty dam around the countertop outside of the sink (I'm assuming it's upside down here) and fill the moat up with the chemical. Let it do its work. Be VERY careful of this stuff or any other chemical likely to do any good. Work outside if possible, do not breath the fumes, and keep away from any source of ignition. If heat seems to work, heat the sink aggressively and let the heat transfer to the adhesive. Once the adhesive is softened, slowly start to pry around the rim with a very slim tool -- I'd drive in single-edge razor blades all around.
Otherwise, I like the idea of breaking the sink up. That will allow you to apply more concentrated force to separate the smaller piece of sink from the countertop. If it's a pure porcelain sink, I'd use a diamond-blade wet saw to cut it off about an inch from the countertop, all around. Then slice it down through to the countertop in 1/2" slices all around. You might then be able to chisel out all the individual pieces. Chisel from the inside of the rim to minimize the chance of chipping off chinks of granite.
If it's a cast iron/porcelainized sink, it's a different ballgame. The upside is that heat might be more effective and easier to apply, but other than that, it's all downside
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Good luck. Cass's suggestion to contact an experienced installer is a good one. The guys that installed my vanity bowls used Alex caulk, which seals up pretty good, but isn't impossible to remove.