You can’t really. An e-mail address in your Constant Contact account tells about your relationship with its owner, the contact. If a recipient becomes fed up with your newsletters and unsubscribes, this information must stick. You must not be allowed to simply delete the address and start over, pretending that nothing has happened.
When you “delete” an e-mail address or a contact using the CtCt website (called GUI) it’s actually only hidden, remaining in the database. It no longer counts towards your quota so for all practical purposes, we can call it deleted. Now, how do you do that with API?