I have this begonia with a really long thick stem which has a lot of growth on it,can I cut it safely and make a new plant?
Yes you can cut it and make many new plants. I would not stick the cut ends into soil until they callous over a little bit. You can lay it horizontally on soilless mix or Perlite while it is callousing where it will probably root anyway. Cover the cuttings with some kind of humidity dome to speed rooting (watch for rot). You can also cut it into several stems (have several nodes on each stem) and treat the same way. If you do cut it into several stems and decide to stick one end into the soil make sure it is the bottom end.