You can cut it anywhere. If your going to trade it, make sure you cut a tradable size.
As for attaching it, I use super
glue (gel type).
Find a piece of rock you want to attach it to, blot it dry with a paper towel.
Add a few drops of the gel on it, let it form a skin (usually 30 seconds) and hold the frag to it (outside the water) until it sticks.
place back into the tank.
Like stated before, the parent will recover in about 1-2 hours.
the new frag may take a few days to come around.
When I trim my toadstools, the new frags take about a week.
PP me if you need any more help.
don't be afraid, just have a good sharp knife.