I am not aware of a solvent for silicone sealer that is not destructive to whatever the silicone is stuck to. I've looked before and there was none. We asked for a killer sealer and that's what Dow corning gave us.

I'd get a box of single edge razor blades and take the long, slow way around the sink. The blade might reach through the bead of sealer or at least it will reduce the sealer adhesion area enough to break the sink free with brute force.

When you do get the sink free you'll have a tedious job removing the old silicone bead but the razor blades will help there too.

Let us know what works...

Remove the fixtures attached to the bottom of the sink.
Set a hydraulic jack on a 2x6 the interior width of the cabinet, and between another 2x board lodged against the bottom of the sink.
The sink weighs about 110lbs. so you'll need to relieve that load +.
The silicone is flexible and you should be able to see some deflection began.
You'll know when you began to break the seal.

Since the best use for silicone is 20' deep in a landfill, unopened, Use POLYSEAMSEAL when you set the new sink.