You can remove content from your site using the HTTP method DELETE. Since you don't want just anyone deleting content from your site, you'll want to keep permission limited to trusted users.
With Drupal 8, you can provide REST services to interact with your site’s data, and you don’t have to rely on contrib modules to do it. This screencast is the first in a series demonstrating how to configure such services.
It is easy to test your website's functionality using Behat, a PHP framework for BDD (behavior driven development). This video quickly goes through the configuration of Behat, Mink, and Selenium.