WordPress generates a large number of RSS feeds. For a single post the URL for that feed is the single post URL plus /feed/ or ?feed=rss2 if pretty permalinks are off. If you try that you will see the comments feed, though, and not the post itself. To get the post itself add ?withoutcomment=1 or &withoutcomments=1 and you will get the post content itself. Have your other site request that feed, whether by AJAX or some PHP function like curl— whatever you have available to the requesting site– and process the XML to display it however you like.
