Cladiella and alcyonia are somewhat transparent, more delicate or jelly looking treelike corals with lots of small fluffy polyps. They seem to enjoy a light to medium light current. They look like they might deflate or ooze out liquid or gel if you cut them.
There are nasty rumors "out there" that cladiella WILL deflate, shrivel up and die if you cut off a branch! I don't know how this got started but I've even seen it in print! Don't believe it! Don't get alarmed! It's a bunch of "bunk, an urban legend, if you like. To prove it to yourself, try the following: Take a sharp pair of scissors or a razor blade and just slice off a branch anywhere. What you'll see is nothing more than the parent coral, and the piece you cut off, retracting their polyps and shriveling up a bit, kind of like they may do at night anyway.

Don't worry, even with a major cut, they'll come out of it after a day or two. I have better success with small and medium size branches than I do with large ones. Very large branch cuttings can sometimes be a royal pain. Take the cut branch out of the tank and put it in a glass bowl of tank water. Take it to the kitchen counter and proceed to sew it onto a rock with a needle and fishing line. Don't worry about taking it out of water. It has plenty of water inside to keep it alive for quite a while.

Now, here IS the problem with cladiella type corals: They are slimy, jelly-like and fishing line can tear through their skin. They can at times be prone to protozoan attack (slime-out) while attaching to a new rock shortly after cutting.
I hope I didn't just scare you off. These problems can be overcome if you know what to do. Just think of corals as mostly plant-like, and imagine that you are working in a greenhouse making cuttings of plants. Not every one of them will take root and grow, but if you know what to do and how to care for them the first two weeks after taking the cuttings then you will have a high success ratio.
Nurserymen don't expect 100% success with plant cuttings but they expect 90% and higher with most species. As a coral gardener, you can expect this too, if you use good techniques. Since fishing line can slice through the coral, you should consider placing the cutting in a depression in the rock you choose to attach it to. This keeps the fishing line from cutting right down through the coral to the rock when pulled and tied tight. It also keeps the coral stump from sliding around. If the rock doesn't have a depression, I drill a slight hole with a masonry drill bit just wider than the coral's stump.
If the colt coral branch is small, I only sew one strand through it to hold it in place in the depression in the rock while it attaches over the next week or two. If the branch is thicker and longer, maybe 5-6 inches long, then I sew a second strand through it, making a cris-cross. This adds stability while still allowing the coral to expand and contract.

The first few days is when the new cutting might secrete a white pasty slime around the freshly cut base which is a feast for protozoans. Once protozoans get started eating this, they multiply and keep on eating live coral flesh too. The whole coral can turn to goo - a slime-out. Use a turkey baster to blow the white slime away, especially from cladiella and alcyonia, each morning and night. Once this is gone, you're probably "out of the woods."
However, If the polyps stay retracted and turn very dark, start decaying, sloughing off or turning to goo after a day or two, this also means that you don't have enough aquarium water movement to keep the slime cleaned off.

Leathery sinularia or finger leather corals don't seem to have much of a problem here, but water flow is still important to prevent a possible slime-out. The trick with cladiella and alcyonia is to have enough aquarium water movement to wash away the material which sloughs off but not so much as to slowly blow these extra soft corals off of the fishing line.

LeRoy Headlee prefers silk thread instead of fishing line because it disintegrates after about three weeks. He's had fishing line come off of rocks and get sucked into power heads, ruining them.
Rubber bands have also worked for me. I cut off a branch of the colt coral just under a fork in the branches, then band the forked branch into a depression. These corals expand and contract a lot and some softer ones can work their way out of the rubber band or can expand so much that the rubber band cuts through them. I still prefer fishing line. It works well if you use it right.
You may want to try two or three small (2"-3") cuttings first before cutting up or pruning a large overgrown coral. This will let you see if you really have the knack before taking the big plunge.