You're right, not much info online. I had to go all the way to the U.K. to find anything helpful. Here is a link that might be useful: British Cactus & Succulent Society

First, you need to know that this plant (and all other Euphorbias) has a very toxic sap that is a powerful skin and eye irritant. If it gets in your eye (e.g. brushing face with back of hand), it can cause temporary blindness. Be careful never to get sap in your eyes, or leave it on your skin. E. tirucalli has a particularly bad reputation for toxic sap, so be careful! Cut at branch nodes. Staunch the flow of sap with lukewarm water. Repot into an 8-inch container using Cactus and Succulent soil (or regular potting soil) mixed 1:1 with perlite, gravel, or pumice. The idea is to make a free-draining mix low in organics, but with more than 50% inorganic particles in the 1/8 to 3/8-inch range. This plant wants as much sun as you can give it. Growth will be much slower indoors. Allow the pot to completely dry before watering. Fertilize 3-4 times a year with any balanced fertilizer at 1/4 the normal strength. Happy growing!

I don't grow this plant, so I can't offer you any specific advice. I am sure you will be asked what type of soil is in the pot. Many problems start there, as most succulents prefer a gritty, fast draining growing medium. The name of this plant is Euphorbia tirucalli. I hope your research told you that this type plant has toxic latex sap. It can cause dermatitis by contact with the sap. Some people are more allergic than others. If it gets in the eye, it causes excruciating pain usually needing medical attention. So now that I've scared you, just be careful in any pruning. Wash your hands and implements well and don't touch your face when trimming or repotting. Spraying any cuts with warm water will stop the flow of latex. Just a little knowledge beforehand to avoid problems! Good luck with your plant!

No water till roots form. I know that can be hard sometimes, but it's important with most succulents. This is a Euphorbia and Euphorbias can take forever to root, and I mean forever. You know what you may want to do? Do a little test, cut off small pieces of your plant. Try to root those. I have a feeling your "cuttings" may be to big. All the plants energy is trying to keep that big plant alive. Instead of sending energy to form roots. Does that make sense? Sometimes I have a hard time explaining myself:). ps- the white goo that comes out of Euphorbias is toxic so keep away from skin and mucous membranes.