1. To split off, disconnect, or become isolated (from other people or things). My friends and I separated off from the tour group to look at a different exhibit on our own. The power unit keeps separating off. We'll need a new way to keep it attached to the machine.

2. To remove and isolate someone, something, or a group from one or more other people or things. In this usage, a noun or pronoun is used either before or after "off." I had to separate the troublesome student off from the rest of the class. Please go through that huge stack of books and separate off the ones that you want to keep.