As it has been dealt before, there is a bug (that is supposed to be solved in versions from 2.2.0 on) that causes groups duplicity when you duplicate an activity.
It's related to bug MDL-29350, that had been parched for versions under 2.2.0.

Well, it seems that it's still happening. We use Moodle 2.2.1, and we are having this exact same problem (maybe because of some kind of specific setup or corrupt component?).