How would you cut and installed corian? We cannot get a router in the location and it is up against a cabinet. Can a sawsall be used?

Almost any wood cutting, and any carbide tipped blade will cut Corian. I would not consider a sawsall because you will not have enough control to make a precise cut. Further, most sawsalls have a 1" stoke. You will most assuredly be damaging what ever is beneath or behind the Corian.

I would start with a circular saw and a 40 tooth blade. Set depth of cut to just cut through the Corian. Use straight edge glued to the Corian for a guide. You will want to make a straight, precise cut but you don't want to go too slow. Corian can get to hot and melt if you cut to slowly. I would then use a saber saw to cut where you can't reach with the circular saw. An oscillating tool (Multifunction Tool) will probably cut the Corian but will be slow. The oscillating tool will give the most flexibility and precision.

Describe your project. Most to the time Corian is fixed to the cabinet with caulking or silicone. You may be able to remove easier than you think.