The mistakes of fragging sure are. I used bone cutters to remove my hammer from the frag plug and it shattered it's skeleton, killing it.
RIP cherry corals gold flake hammer
That's why I usually gently "saw" the hammer base (dead skeleton) with a pair of scissors. I've been tempted to make some micro hand saws with jigsaw blades or a pumpkin cutter blade. Then attach that to rock or plug with super glue and/or putty.
I do most my fragging in tank, softies and LPS. If the are small zoas, etc I'll take them out and attach to a plug out of tank . I do most of my work on paper towels. If I'm using putty it will make your skimmer go crazy for a day, so I take the collection cup off. I dislike using putty in tank, never seems to stick well, I'm usually making a base in the rock for the stem of a frag plug to sit, then super glueing or friction fitting the plug into the putty hole.
Loose Discoma mushrooms are best to put in a dish with rubble in tank, let them naturally attach to that, then superglue that to a plug. I do similar with zoas, but that can be directly glues to plugs.
I've had a hard time with nepthia. It doesn't seem to like super glue. I will take a big piece cut with siccosrs, pierce the base with a toothpick, wrap the toothpick to a small rock aligning the cut base so it can naturally attach to the rock. Sometimes it works. It can attach to rock if it is laying on it for long enough. I've moved it to different places in my tank that way.
I once cut a toadstool leather. Make a couple of wedge cuts like a slice of pizza, don't remove the slice, let the cuts heal, do a final cut. Take the piece and pierce that with a toothpick, wrap to a rock. I think I was able to glue that but wrapping it to a rock helped keep it in place.
Most of my techniques are from being glued to reef forums for too long

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