These are the ways I have killed them.
Method one:
Buy Meriodic Acid from Home Depot, and a syringe from a drug store. Fill the syringe up with one CC ( BE VERY CAREFULL) and inject it in its mouth. You will have a "kill radius" Kill one to three aiptasia's with the meriodic acid a day. Put at most one cc of the acid in your tank a day. Do this with the rock still in the water. Too much of the acid will lower your PH. And by all means keep the acid away from children.
Method two:
If you can easily take the rock out of the water, then get a clear mental image of the rock and where the Aip is on the rock (Draw a diagram on scratch paper will help too). Take the rock out and the use marine salt to smoother it. (Once the rock is out of the water it is much harder to see where the Aip is) Pack that salt onto the area that has the Aip and leave it there for 5-20 minutes. You will have a "kill radius." Meaning you well loose all forms of life where you put the salt. Then rinse the salt in water and place back in your tank.
Method three: ( I havent tried this yet)
Put a small rock ontop of an Aip. The Aip will supposedly move to the small rock on top, and at that time remove the rock.
Things to watch out for:
Dont try and pick the Aips off with a stick or tweezers or anything. It will just make matters worse. Any particle left behind can regenerate to a new Aip.
Natural ways of killing them:
Racoon Buttlerfly (Will eat Aips but is not reef safe)
Nudibranch Berghia Verrucicornis (Will only eat Aips. the Nudibranch of this kind are not that easy to find for sell and will die after they eat your Aips and have nothing else to eat)
Perperment Shrimp (Will eat Aips and are reef safe and will eat other things, but they dont not eat them as well as the Nudibranch and Racoon Butterfly)
Other methods I have heard of:
They are similar to method one I posted above but just use a different chemical such as vinigar, boiling water, and Sodium Hydroxide (NaOH)
Hope this helps some, and good luck,
B