It's joint compound, commonly called mud, and not grout.
If you are sanding into the tape, you have not applied enough.
It's not a "one and done" product. You apply joint compound and embed tape.
You let it dry (or set, but setting compound is not the usual DIY choice.) Incidentally, USG recommends paper tape as superior to mesh unless you are using setting type joint compound (aka "hot mud.")
You lightly scrape or sand to knock off only the high points and apply more compound with a wider knife.
You let it dry
You repeat that a few times, with larger knives.
You shine the harshest light you can find at low angles and look for defects in the surface. When you reach the point that you can't find any, even after looking again from other angles, you prime and paint.