What's the sink made of? If it's stainless, it'll flex enough to get a sharp kitchen knife under it, run it round, then wedge screwdrivers etc under to hold it up, and keep at it until it comes up. Use folded card under screwdriver blades to protect worktop.
If it just has one of those foam double sided thingies, as above but 10 times easier!
If it's a resin cast sink, it'll be a swine: mine had to come out, but I was replacing worktops anyway, so I cut it out, and bought a new sink. the old one is propped up outside until I can get round to chopping the worktop off it with a chisel, to re-use the sink in the utility I'm supposed to build in our French property.
If the sink is no good, and you want to keep the work tops, have you thought of breaking the sink up with a large and/or sharp hammer? The pieces will be easier to remove than trying to do it whole, believe me. Put an old rug etc in the cupboard below to protect it.
Harvey Smith, R.I.P.
I'm proud to have called him my friend.