Yes! If you’re on the Asana Business or Enterprise plan and thus have access to build custom rules, there is a (fairly new) “Unassign task” rule action to do just what you’re wanting:
If you’re on the Premium plan and thus don’t have access to custom rules, you can use our Flowsana integration, which also has an “Unassign task” rule action and whose rules can be built at any Asana subscription level.
The action of adding the task to the project (i.e. the rule trigger) - did that occur as the result of a human being adding the task to the project, or as the result of another rule adding the task?
Tasks are added by sending an e-mail to the project. E-mails are automatically forwarded from my own account. That is probably why I am set as assignee.
The due date action worked every time. The last instance of the rule running it did not remove the assignee.