Removing / replacing silicone caulk

We have a stainless steel sink (undermount) attached to a granite countertop. Over the years, the silicone caulk no longer creates a tight seal between the sink and the counter...therefore water is able to run down into the cabinet. The sink doesn't feel loose, but it appears to have 'sagged' over the years. Should I remove the old caulk before applying new? I'm guessing the answer to that is yes, but what is the best method to remove the old caulk??



Thanks in advance for any advice!