I'm facing issues in removing EXISTING users from a group in the designer. I

Have you checked that the existing users are direct members of that group rather than members of a different group that has been added as a member of the group?

@philb: Yes..they are members of different group who have been added to the current group(including group too). Does this mean only direct members of the group can be removed?

Yes, if a user is a member of a subgroup then you must remove them from the subgroup in order for them not to be a member of the group. Alternatively, remove the subgroup from the group and they will be removed from the group members.

Is there any error message you'r getting while removing existing user?

As philb mentioned, you will not be able to remove a member of the Child group. And yes the confusion is that you cannot distinguish as who belong to Parent and Child when you list the members of the Parent group.

GroupParent           <-(Parent Group)
          - User1           <-(Member of Group Parent)
          - User2           <-(Member of Group Child1)
          - User3           <-(Member of Group Child2)
          - GroupChild1           <-(Child1 Group)
          - GroupChild2           <-(Child2 Group)