1. Once you've marked all the emails you want deleted, you'll see a line through each email.
2. Click on the "Folder" tab at the top.
3. Click on the "Purge" Icon, a drop down will appear.
4. You can either do a "Purge All Accounts" or you can just purge the specific account your cleaning up.
5. Go to your "Deleted Items" folder, right click, Empty folder and that well clean off all your emails you've deleted.