There are quite a few threads on this site on pruning and repotting. Do a search and you should find them.
As for cutting the caudex, I could not say. Probably nee to post a photo.

I think he/she is talking about placing a nick in various places on the caudex in hopes that it would eventually form a growth/branch. I think it is an excellent question but do not know the answer. I will give it a try on one of mine and see what happens. I don't think it would hurt if you tried it either.