Trying to replace old sink

We are trying to replace our old kitchen sink. It's probably around 30 years old, porcelain lined with a metal base area. The sink is held to the counter by a metal band that goes around the edge and screws from the bottom. The screws are so rusted that they cannot be removed. We are not wanting to destroy the counter top, but are not certain how to get the sink out. Ideas?

I know the access up into where those screws are is awful. If they don't look too far gone, you could spray with PB blaster, and repeat daily for 3 or 4 days. If they are really beyond help, you could try to just break the screws with vice grips, or use a long 3/8 pr 1/2" cold chisel and hammer.

clamps

Depending on which ring and clamps you have, you may be able to just twist the clamp itself to remove it. Some clamps go through the ring and they cannot be twisted. BUT all clamps are aluminum and since you are not worried about the sink you can pry/bend them to loosen the clamp and then remove it.

Perhaps you can get a dremel with a cut-off wheel in there and cut the clamps -- ideally the steel screw.

As HJ says, the clamps are aluminum and you should be able to coax them off with vice grips by bending them this way and that until something fatigues enough to let go.

Is this a cast iron sink, or steel? If the sink is C/I in good shape it would be nice to save it, the ring and the clamps as there is a (small) market for retro sinks out there.