If you need to unsubscribe a contact from getting any messages from your account no matter which group they are in, including future groups, you will want to add their number to the suppression list.
The suppression lists gets checked before sending out any messages and will not attempt to send any out if the number is added to it.
To get started first click on Account to get to your account page.
Next, on the right hand side, click on Suppression List.
Finally, add the phone number to the list and click Save. Add each number on it's own line in the text box.