I could reproduce and confirm this problem, but only when having Joomla SEF on.
It was a SEF link building/decoding bug, as "action=groups&func=save" resulted in only "save" segment being generated instead of groups/save, which didn't work when the auto-selected menu was not exactly action=groups (but e.g. action=allgroups)
forge.joomlapolis.com/issues/8077
This bug is now fixed, and a nightly GroupJive released.
To upgrade, as usual, backup, then go to admin "Community Builder" / "Plugins" / "Install & Update", then click the "Refresh" button at bottom right, and then the "Update all" button at top right.