Wordpress stores data such as the primary uri and the active theme in the database, so what you are suggesting can't really be done (at least not without hacking one of the wp-config.php files).
What you can do, as a workaround, is have a second wordpress site that imports the posts from the first via an RSS feed plugin, such as FeedWordPress.
You should ensure that the second site is configured NOT to index in search engines, else both sites will suffer in search rankings.