That's funny you've never shot a grouse. That's the very first thing me, all my cousins, all my buddies, etc. ever killed as soon as we got a license. We have an old single shot .410 that goes with whatever new kid needs to go shoot something. Everyone in my family started by killing grouse with that thing - usually somewhere between 10 and 12 years old.
Anyway, this might be debatable, but the Judo points and field points usually let your arrow go right through them. My buddy and I used the big rubber blunts and he shot one, the arrow didn't completely pass through and the damn thing flew off with it. It only happened once, though, so I don't want to say that every time you shoot a grouse you risk an arrow. That's probably overstating it. I use Judo Points, though, so I can stump shoot with the same arrow when I'm walking around in the middle of the day.
When I shoot one I usually run as fast as I can to it to make sure it doesn't sort of recover and hide in the brush (just in case, they usually don't go anywhere.)