How can I stop a Rule action from being executed, programmatically?
Once happened, you can't stop an action.

The only thing you can prevent from happening is executing the action at all. In case of e-mails, you can only stop an e-mail with rules if it has been sent by a rule. Then you need to add a condition to that rule to prevent it from executing the action that sends the mail.

To prevent a mail that is sent directly in the code, you need a custom module, implement hook_mail_alter() and redirect it to a dummy address, you can't really stop it there either.