Although you could cut it now and likely not harm it, I would wait until its more established and attached. Try attach it to a rock that removable for cutting, although I have done it in a tank. I used mono fishing line and a needle to attach my leather frags.
Cutting in ones tank, besides leaky corals, can also bring about abuse from some fish.
My cinnamon clowns would ravage your hand in there. As mentioned, my sailfin use to help me propagate. In that tank I had a pair of mated yellow tail damsels. They would bite my hand everytime I was in there cutting.
My prefered method was to remove the corals to a large bowl of tank water and cut there. Have another bowl of tank water ready and put the newly attached frags & pieces of rock in there after attaching them. Always watch the water temp. & such in the bowls.
Most polyps and muchrooms can just be propagated by placing rock rubble beside them and letting them grow on such. Star polyps can also be done by getting them to grwo on glass and then just peel of slabs of purple mat by running a blade on the glass.