Only process admins, project admins, and task admins can delete documents from a project.

Deleting a document will remove it completely from the project.  Here's how:

  1. Open the Project Documents or Task Documents view where the document is listed
  2. Hover over the document that you want to delete.  
  3. Click the X button that appears.
  4. Confirm the deletion

Note: If you instead delete the task where the document is associated, you will be able to recover the task and document from the Recycle Bin.