For an undermount sink, a jigsaw will make a fine rough cut in butcher block, but you need at least a 1 1/2 horsepower router with a 1/2" bit and a jig to get it perfect. I'd test for burning and tear-out on a scrap; you may have to run the router counterclockwise.
If you've got the room in the cabinet for the clips you can use the method above, if not, cut and finish the cut-out, drop the sink into the cabinet, install the top, install a Hercules Universal Sink Harness or Sink Strap, apply silicone and strap the sink into place.
Q