You can manually unsubscribe contacts by going to the contact detail screen (by clicking on the contact’s phone number). You can then change the contact status by clicking on the status drop down and selecting UNSUBSCRIBE, and then clicking save.
This is useful if the contact doesn't unsubscribe properly, for example replies with "STOP texting me!".
The manual unsubscribe will be remembered as long as you don't delete the contact and re-upload it. If you simply upload the contact again without first deleting it, the system will persist the status.
See contact detail example below.