If you are still on the old email format----------
From the Inbox page, go to Preferences>>>>>General>>>>>Versions. Full is the default. Click on Lite to set it. It will save automatically. Go back to Email. In the Folders pane to the left, click on "Edit". Then you will see the checkbox to clean out the Inbox folder. Just keep in mind that you can't undo this operation. Once you do it, everything is gone permanently.
If you are on the new format, just right-click on any folder and you will see the option to empty it. It will say "Delete all messages."