If you need to remove a constituent from all lists AND mark their record as Unsubscribed so that they will not receive any future email marketing communications and cannot be added to any email lists, then go to the Contacts Page and click on ALL RECIPIENTS.

From the grid, search or filter the list to find the constituent and check the box under the "Unsubscribe" column. This will unsubscribe and remove them from all lists, flag their record and change their email status to Unsubscribe.