How to get sink off of countertop?
First check and make sure that you have removed any fasteners under the counter top holding the sink in place.

Next, you can try wedging a putty knife in between the lip of the sink and the counter and working your way around. Depending on the adhesive used, a solvent like paint thinner may help. A heat gun or hair dryer may also be able to soften the adhesive.

If you're still having trouble, you can always take the sink off with the old counter top and work on it later.