I am a carpenter and a millwork installer for over 10 years. Sinks can be hard to install in dense material like solid wood. You will burn through tons of blades using a jigsaw or saws all. I am hoping that your sink is not an undermount sink, so you can hide the marks this is going to make in the wood!

The best way I have found is with a small router called a laminate trimmer. They are not expensive and a really handy tool. Because they cut by spinning the blades parallel to the surface, you can get a nice clear cut that is 90 degrees to the counter top. I would get a router bit called a “flush cut bit”. This type has a ball bearing guide at the top ( if you hold it so the blades are facing down) that is the same width as the cutters. This allows you to cut to the line and then follow that cut to go deeper.

First, I would use a sharp knife and cut a mark in the surface along my line. I would set the router to cut 1/4” down. Then I would carefully rout to my line around the whole area. Then I would push the bit down until the ball bearing was touching the cut I just did. The next run around the ball bearing and cut would then follow the first cut you did. You just keep moving the router bit down a little at a time until you get through. It looks like the counter is about 1 1/4” thick, so get a bit that has a least that blade length.

Be careful, and go slow. Also, make sure that you go counter clockwise to the line as this will make a better cut.

This is how most installers I know do this kind of cut.

Good luck!