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Scroll down and tap Settings. Scroll down and tap Delete Site. Tap Delete Site (iPhone) or YES (Android). Enter your site's web address when prompted. Tap Permanently Delete Site.
This gear-shaped icon is near the bottom of the page. It's at the bottom of the Settings page. Doing so takes you to the confirmation page. Type in the full address for your blog as indicated by the text at the top of the pop-up menu. For example, if your blog was named "pickledcucumbers.wordpress.com", you would type pickledcucumbers.wordpress.com into the text field. It's the red text below the text field. Tapping this option permanently deletes your blog from WordPress.  On Android, you'll just tap DELETE here. It may take several days for the blog to disappear from Google archive pages.