The mirror variable is local to the method, and will ALWAYS be unitialized in each call.
Passing mirror as an argument to the method is a very good option.
EDIT: If you can't modify the method signature, can you create a private method and call that to perform the recursion?
"I don't think this is possible without passing mirror as an argument into the method or defining it in the class definition... but I want to make sure."
Correct, that would be one way to do what you want, as mirror is not a recursion invariant.
The other way would be that your recursive algorithm clones just nodes, not entire subtrees.
It's rare to see public recursive functions like that. A better solution might be to have the public method that creates the object, and then calls a private function which is recursive that just makes the necessary changes.
It's generally difficult to have the recursive function signature match what you want to show to your clients.
Uri's answer is the best.... refactor it into a private method and simply initialize the mirror then invoke the private (recrsive) method passing mirror as a parameter.