Replacing drop-in stove with free-standing stove. How do I modify the kitchen cabinets?
Assuming there are vertical side-cabinet panels at the areas you want to cut out (ie, you won't be leaving a section of countertop or shelves hanging in mid-air) and that the countertop is a laminate over wood(-ish), then a handheld circular saw can make the bulk of the cuts, with a jigsaw to get the back corners. You can screw a straight piece of wood to the area that's coming out to act as a saw guide. Keep the saw tight against the guide as you cut, and that'll be as straight as the guide is.

Now to make it nice-looking, you have a few options. Big box home improvement stores will sell an end-cap of laminate that matches the countertops they sell, it can be glued on with contact cement, assuming it matches your counter. If they don't have one that matches your counter in color, check to see if they have one that will match your new stove. (It's not great, but it's better than bare wood.)

Home improvement stores will also sell a strip of flanged plastic or metal that is meant to cover the gap between the countertop and the stove (I believe one company calls it a 'crumb guard').