If you're lucky, the person who installed your Corian countertop didn't actually glue the 4-inch backsplash to the wall. The installation instructions for this type of backsplash call for adhering it to the countertop -- not the wall -- and sealing the edges with caulk. Not everybody reads instructions, however, and yours may be stuck to the wall with silicone caulk or construction adhesive. If so, you won't be able to avoid damaging the drywall when you pry it off. Fortunately, you can repair any damage that occurs with inexpensive drywall supplies.
Things You'll Need
Stiff putty knife
Drywall joint compound
4-inch drywall knife
Cut through the caulk sealing the backsplash to the wall with a utility knife. If you're just trying to remove the backsplash and want to leave the counter in place, cut through the caulk sealing it to the counter as well.
Locate the wall studs behind the backsplash with a stud finder. Tap a flat bar behind the backsplash and in front of the stud nearest the end, using a hammer. Pry the backsplash out as far as you can.
Work your way along the backsplash, prying against each stud in turn until you reach the other end. At this point, the backsplash will be separated from the wall but may still be attached to the counter.
Tap a stiff putty knife between the backsplash and the counter at one end of the backsplash and pry upward. Move along the backsplash, prying it incrementally until you reach the other end, then remove it.
Scrape the glue off the wall with the putty knife, pulling off paper if necessary. Cut off all the torn drywall paper with a utility knife.
Fill the areas of exposed gypsum with drywall joint compound by troweling the compound in with a 4-inch drywall knife and scraping it flat. Let it dry, then spread on two more coats, letting each dry and scraping it flat. Sand the final coat with 120-grit sandpaper, then prime it with drywall primer and paint it.
If you're removing the entire counter, you may prefer to leave the backsplash attached to it.