There is a way to upload an excel spreadsheet of unsubscribes, or people who do not want your mailing, to Constant Contact. You will need to click on an option under My Settings in order to do this.
If you click on My Settings, then scroll down until you see the Contact Settings pane.
You will need to checkmark this box in order to upload the unsubscribed contacts.
Once you enable that feature, there will be an option on the Contacts page, under Add Contacts, to then Add unsubscribed from file.
Hopefully this helps, and here is a link that will walk you through the whole process in more detail!
... View more