To permanently delete an article you must first move it to the trash and then permanently delete it from the Trashed section of the site.
Move the article to trash
Follow the instructions in the following article to move the article to the trash:
How do I remove an article from a chapter?
After you have done that follow the instructions below.
Eric
This is a bit painful to have to remove items one at a time when you have 20 pages of trashed items. There should be an "empty trash" option that removes everything.
Amie Barder
@Eric: Thanks for that feedback - I'll add you as a +1 to that request.