How to render a specific page as if the currently logged in user is not logged in?
For an anonymous user, the easiest way to do this is to use a second browser and visit the specific page without being logged in. An alternative to that would be to logout (but that seems to contradict with "user is logged in).

For other (none anonymous) roles, you can use the Masquerade module (for sure). You might consider using this module also for "anonymous users". However be aware of this note on its project page:


  Any previous support to masquerade as "anonymous" has always been buggy and hurts performance on larger sites. To masquerade as anonymous users, logout.


My recommendation therefor is: open that page in a 2nd browser, without being logged in.

PS: works for any currently supported release of Drupal.