Must We Cut Off Means of Demons Communicating with Each Other When We Cast One Out?

NO!

This foolishness isn’t in the Bible.  You’d only hear it at a Special Weird Deliverance Seminar.  There are NO cases in the Bible where ANYONE “cut off communications” between spirits in or out of someone when one or more spirits were being cast out.  If they didn’t need to do it in the Bible, neither do you.