The finish is gone in the corian sink countertop in my bathroom. Except for the sink the corian is in good shape. Can I cut out the sink and replace it? Or do I need to just remove the whole thing? The sink is stained, scratched and ugly, can't be cleaned by any amount of scrubbing.

Depends on size of sink and type. U may be able to get a top with integrated sink for about the same as just a sink.

Line the area to be cut with duct tape. This will reduce chance of corian chipping. Cut the straight areas around sink to the size required using template that comes with new sink. Use a power saw with a 42 tooth carbide blade. Cut corners with a saber saw.

Support the sink being cut out with a piece of wood under drain hole and a piece across opening on top. Tie wood together with a length of rope.

Chuck

The sink is stained, scratched and ugly, can't be cleaned by any amount of scrubbing
A new surface can be obtained by sanding. Corian is the same color and material all the way through.
Sand with 120 grit until all scratches and stains are removed. Then sand with 240, 400 and 600 grit.

Harold is right .

If you find that it is not the same as you sand it is not Corian.

As to cutting out the sink. A router would be a better tool to use as the corners need to be radiused. It is also best to sand the edges of the opening to eliminate any tooth marks.