Protect your counters. Find some cardboard, drop cloths or even newspaper to place on your counter to protect it from getting nicked or scratched. Use painter's tape to secure the protection to the counter. Be sure not to tape onto the caulk, but get as close to it as you can.
Cut into the caulk at a 45-degree angle. This will give you two separate strands of caulking to work with. One will be attached primarily to the kitchen counter while the other will be attached to the wall. It is fine if you cut into the wall a little bit, just try not to cut too deep.
Score the drywall. Use a knife or razor to gently cut across the top of the caulking. Try to apply as little pressure as possible so that you do not do noticeable damage the drywall. This scoring process will give you an even seam so that when you remove the caulk from the wall, you will have the least work to do to make the wall look good again.
Cut away the caulk from the counter. Hold a razor blade parallel to the top of the counter. Cut under the edge of the caulk and slowly start working the razor along the surface of the counter. Have several razor blades handy because they will get dull and messy pretty quickly. After a while, you may be able to pull the whole piece of caulk up as one long strip. Use needle nose pliers and slowly pull the caulk away from the counter.
Peel away the caulk from the wall. Use the razor blades again, but be very careful cutting around the wall so that you do not have to repair much of the wall after you remove the caulk. When pulling off the caulking, pull it down and away from the wall to prevent tearing the drywall paper or paint.
Clean up any remaining caulk. Use a knife or razor blade to clean up anything that is left. If you still have a lot of caulk left, try a commercial caulk remover. Be aware that caulk remover can damage your counter or wall. Scrub down the counter and wall with an abrasive sponge once all the caulk is removed to clean up any remaining residue. If the caulk was old and brittle, wash off the counter and wall with a damp cloth.