The sink has one existing hole, and 3 knockouts which are cut about half way through the material.
What are the best tools, and techniques for removing fixture knockouts on a composite granite sink?
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As brutal as it seems, the prescribed method by FRANKE is to use a blunt ended large punch and a hammer. Set the punch dead center in the cutout and strike it soundly. Don't be too tentative, give it a good shot! Place the punch on the top. If you have a carbide hole saw, pilot a small hole dead center from the side already drilled then finish it off from the top, using the pilot hole.
When I first saw my plumber do this on a kitchen job, I cringed, but it worked well. Weren't there any instructions with your sink? I'm just relating the way FRANKE recommends, maybe your brand has a different method.