To remove a group from Schoolrunner for all users, find it on the Groups page and click the gear icon next to its name. Click the "Deactivate Group" button to remove it from Schoolrunner.
If any other users are subscribed to the group, or have it starred, you'll see a warning asking you to confirm your action. If deactivating the group doesn't affect any other users, the group will be removed immediately.
If you want to stop getting notifications for a group (your subscription may have been created by someone else), and stop seeing it in dropdown menus, you can un-star the group instead of deactivating it, which preserves the groups for other users. You can manage all of your notifications on your user settings page.