What is this type of interior wall?
That's a normal wall, sheetrock over plaster. That's how you save money when you want to renovate your home with plaster walls in bad shape, you just screw gyp board on top instead of paying for demo/dumping then gyp.
run your finger around the back side of the plaster inside the wall, you should feel some lath or if the lath is nocked away, you should feel flat/bulge/flat/etc.
Also, that's not insulation. Insulation is like cutting through butter. That's plaster. Delicious dusty plaster.
It's fine to cut into with a drywall saw, and it's normal that it will destroy your drywall saw. Most people just use whatever they have on hand, and you just have to decide which tool you want to destroy.... you can get purpose made masonry blades for your tool of choice, but then you have the tool of choice cost on top of the blade, and a drywall saw is so cheap to begin with. Cost of &quot;replacing&quot; drywall saw you already have if you're really sad it's not sharp as new versus: Cost of reciprocating saw and masonry blade; or, Cost of masonry reciprocating saw blade and replaceable blade handle that accepts that type of blade; or, Cost of oscillating multi tool and masonry blade.