No, "self-destruct" isn't a way to clear out the 12,667 unread emails from your entire inbox at the touch of a button. (Seriously, though, stop procrastinating the zero-inbox goal you set for yourself on New Year's.)
But Gmail did release a few new features over the summer (we know, it flew under our radar, too...) to send emails that will "self-destruct" for better privacy; ones that can't be copied, downloaded or forwarded; and messages that can be set to "confidential mode" and require a passcode to open.
Here's how it works: Sign into your Gmail account, then click the Settings gear icon. Select "switch to new inbox" (if you're already using the new Gmail update, you're good to go). Once your inbox reloads from upgrading to the new format, click "compose" to start a new email.
At the very bottom to the right of the send button, you'll notice a tiny little padlock-and-clock icon. Click it, and you can set up an expiration date so the email will disappear after a certain time period. You can also select the option to require a code sent via SMS text to the recipient's phone in order to unlock it. Emails sent in confidential mode disable normal print, copy/paste and forward features. Attachments can't be downloaded by the recipient, either.