Spray caulk softener on the silicone caulk surrounding the sink base. Let the caulk softener sit and soak into the caulk for the amount of time recommended by the manufacturer.
Wedge the tip of a putty knife underneath the softened caulk. Peel away the caulk in a line. Discard the old caulk. Scrape away any residual caulk you see with the putty knife.
Turn off the water supply. Unscrew and remove the sink's drain pipe. If your sink has a garbage disposal, detach and remove it from beneath the sink.
Remove any sink clips holding your sink in place.
Slide the blade of the utility knife underneath the sink rim, loosening the silicone adhesive below the sink's rim as much as possible.
Pry the sink free from the countertop with a pry bar.