Mushrooms can be sliced of the rocks using a razor blade. There's a catch, though: this won't actually remove the shroom from the rock. It'll just make more shrooms.
To remove the shroom from the place you don't want it, you'll have to kill it.
You can use a kalk-paste to smother/burn the shroom stump. I've done that. Just make sure you turn off the current in the tank.
To attach a shroom frag, you can use a rubber band, fishing line, bridal veil, or that thin plastic netting that they use to bag onions. After you secure it using one of those methods, you just wait for the shroom frag to attach. I won't tank long.
Superglue will work underwater, but it's messy. Epoxy putty might work, but it's hard to get the shroom to stay put.