Does cutting aiptasia kill it?
No. Cutting or clipping aiptasia usually makes more of it. The stalk left on the rock grows a new head, the piece you cut off can reattach and grow, and any tiny bit of foot left behind can turn into a whole new aiptasia.
We cut aiptasia on purpose
Every reefer is trying to get rid of aiptasia. We're trying to grow a lot of it, because it's the only thing berghia eat, and for a while it was growing so slowly it was driving me crazy. We tried everything people said would help: rubbing the rock with a toothbrush, scraping, pulling, and clipping just the tentacles.
What finally worked was clipping the whole head off. The stalk grows a new head, and the clipped head reattaches somewhere new. Two aiptasia for the price of one!
Clipping the head off: the stalk grows a new one and the head reattaches (starts at 2:23)
That's great news for our aiptasia farm. It's the opposite of what you want if you're trying to get rid of aiptasia in your display tank.
Why cutting backfires
Picking at aiptasia can make it worse in two ways. Any little piece of the foot left behind can grow into a new one (scientists call this pedal laceration, and it's exactly what we see when we clip heads). And a lot of reefers say a stressed or dying aiptasia can release larvae that settle all over your tank. We haven't seen that one ourselves, but either way, poking at it isn't helping.
What to do instead
Try to leave it alone while you decide what to do, and count how many you can see. What worked for us was berghia, tiny sea slugs that eat aiptasia and nothing else. We wrote about everything we tried (and skipped) here: how to get rid of aiptasia (what we tried, what we skipped, and what worked).