Best Method to Separate Drupal Website from Customized Scripts I currently have 2 small cloud servers: (1) database server; (2) web server.

The web server hosts my Drupal 7 website plus a lot of continually running scripts that process data and hook into Drupal's API functions (e.g. node_save, taxonomy_term_save).

I would like to split up my web server into two servers so that now I have 3 servers: (1) database server; (2) Drupal website server; (3) data processing server.

Since my custom scripts tie into Drupal's API functions, I am not sure how to actually run these scripts from a completely separate server without essentially cloning the web server and just blocking public access to the website on the data processing server.

Any ideas would be greatly appreciated! Thanks!
There's no way to use Drupal Apis from a separate server. Your best bet would be to use the web service module and process your request via json.

You'll have to do more work but on second hand, you'll end up with a nifty setup that'll allow you to leverage many other frameworks such as angularjs, backbone, and even mobile development.