Here is a short and simple tutorial on removing an affiliation with another group.
Go to your group's Home Page.
Scroll down to the affiliation widget on said group's page. If you do not have it installed, you will need to do this in order to manage your group's affiliates.
Click the little pencil icon in the top-right corner of the widget and select 'Edit Widget'
Once the widget is in Edit Mode, click the "Edit Affiliates" button.
A new pop-up window will appear on the screen. This window will have every affiliation your group currently has. To remove an affiliation, click the small arrow next to the group you wish to cancel the affiliation with - then select 'Remove Affiliation'
Finally, click 'Save' to ensure your recent changes are saved.