Only Portal Admins have the ability to permanently delete work. Once you have deleted work, there is no way of getting the work back.
1. Go to Advanced Search and in the Archive drop down choose "All Archives".
2. Select the archived project/work that you want to delete.
3. Click on the 3 dots and in the drop down select "Permanently Delete". Another pop up will allow you to "Cancel" or click "OK" to delete.