For Android, MacOS, and iOS, you can easily deactivate (and reactivate) private Duck Addresses within the Passwords menu in the DuckDuckGo browser. First, select the browser menu, then open Passwords, select the private Duck Address you want to deactivate (or reactivate), and follow the on-screen prompts.
If you’re using Windows or the DuckDuckGo browser extension (and alternatively for Android, MacOS, and iOS), find an email sent to the address you want to deactivate and click/tap the Deactivate button in the DuckDuckGo banner at the top of the email. This will deactivate the address, which can also be reactivated following the same steps.
Prior versions on GitHub.