Joomla allows you to delete articles, you can re-publish deleted aticles if you find that you made a mistake by deleting it in the first place. Deleting an article sends it to the trash and you can re-publish it from the thrash manager.

This article shows you how you can delete an article from the thrash can which is to permanently delete an article in Joomla. Once an article is deleted from the trash can, it can no longer be recovered.

Step #1. Move articles to trash
Go to Content > Articles.
Select the articles you want to delete.
Click Trash button.

Step #2. Empty Trash
Click Search tools in articles manager.
click Select status ana choose "Trashed".
Select the articles you want to delete permanently.
Click Empty trash button.

Source: https://www.todhost.com/knowledgebase/713/How-to-permanently-delete-an-article-in-Joomla.html