how to delete emails in a smart mailbox

First, it is essential that you know that messages are not stored in a Smart Mailbox. Messages are listed in a Smart Mailbox from wherever they reside, but they are actually stored only in a "real" Mailbox. If your Smart Mailbox has the checkbox set that includes messages from the Trash, then putting a message into the ("real") Trash Mailbox will not delete it from the list in your Smart Mailbox. Unchecking that box or emptying Mail's Trash will.

Expect significant delay after you take an action before that action is reflected in a Smart Mailbox. Every time you change anything, your Smart Mailbox has to search through all your emails (in all your "real" Mailboxes) to compose a new list. Until the search completes, the list viewed in your Smart Mailbox will be incorrect and possibly misleading.

--Gil

There are no messages in a smart mailbox, so you can not delete them. But you can delete the mailbox itself.