This process was a little bit different for me than it will be for you, but I'm guessing you don't have a round butterfly sink, eh? Usually double-basin undermount sinks have just one hole in the counter, so the subset (dividing area between sinks) is not covered by the countertop. I wanted my subset to be covered by the countertop, though, because we were using our existing sink, and it had holes from previous hardware (the sprayer and knobs) that weren't needed for our new faucet.
Because our sink is so unique, our process of cutting holes for it was different than yours. Typically, you can make a template for the sink by clamping plywood (with a rough-cut sink opening) to the top of the sink (after duct-taping the sink to protect the surface) and then routering out the hole. The bearing edge of the router follows the form of the sink hole while the blade cuts out the shape. This YouTube video shows how simple it can be. We planned on spacing out the sink holes a bit to give space to the miter joint, so we didn't bother tracing the sink exactly. Instead, we measured the holes of the sink and cut out the holes of the template to be placed exactly where we wanted them to be.
The circle was drawn precisely by using a compass made from a scrap piece of wood with a nail hammered into the radial point and a marker fit into a drilled hole on the other end. The next step was to use a jigsaw or Sawzall to cut out the shape, leaving about a 1/4" border along the inside of the marker line. The router would take away that 1/4" border as it cut out the precise shape with the use of another makeshift compass attached to the router. (See below left.)
To cut the holes in the butcher block, we traced the circle from the template and cut out the holes with a Sawzall, leaving a border just like we did for the template above. Then we clamped the Masonite template into place (see below) and routered the cut edge to get the hole to the precise size of the template. At times, the router would go against the grain and start roughing up the cut edge, so then we came at that area from the opposite side to make sure the router blade was always going with the grain, ensuring a smooth cut edge.