I don't know that any special care is needed, assuming they are clean cuts. Seems like a good time of year to do it, next spring the tree will leaf out with enough root to support what used to be bigger.
I will be watching for other opinions, out of curiosity. I'm fond of redbuds, have 2 big ones, 4 several years old (preschoolers) and foster many of their babies to give away.
