There are a few ways to remove Contacts from an Organization Group. The easiest would be from the actual Organization Group page. Just go to Settings and then select "Manage Organization Groups" to bring up the main Organization Groups page. If you click on the Actions button in the upper right, you'll see the option to remove all Contacts from the group.
Scrolling down, next to each Contact, you'll also see a trash can icon, which you can use to remove specific Contacts from the group.