What I am trying to accomplish is removing Skype from a user. I have removed Skype license directly from the user, but I have Inheriting licenses from a group that includes Skype. It appears that the Inheriting licenses from a group is overwriting anything that I have assigned or removed Directly. Is there a way to break the inheriting from group in Azure Group Based Licensing without removing the user from the group?
If you have different requirements then you'll need to have different groups set up to handle the license assignments. There's two ways you could do this:
1) Have one group for the entire license suite, and one group for everything except Skype. Place users in one group or the other, but not both.
2) Have one group for the base features of the license suite, e.g. O365 ProPlus, EXO, SPO, and then create additional groups for the optional services, e.g. Skype (when I say "optional" I mean those that your org isn't going to provide to everyone). All users go in the base group, and then they get put in additional groups for the optional services. Groups-based licensing is cumulative, so you can have users in multiple groups and their assignments will be the combination of all of those group license assignments.