Try hitting the enter key or spacebar. Sometimes you find situations where a dialog box just ends up extending beyond the confines of a low resolution display, and especially with dialog boxes that are populated with data from the program, so the developers would have no way of knowing how big it may become in circumstances like yours.
But enter and the spacebar are two pretty common keyboard shortcuts for controls. Enter is usually the same as clicking whatever is the default button on a dialog box or window, and the spacebar will be the same as a mouse press for whichever one has the halo around it.
You can also try the Esc key, which is a common keyboard shortcut that loosely aligns with "cancel".
If all else fails, first I'd take a screenshot and send it off to Apple so that they can fix it in some future release... If they feel like it anyway. Then you can force quit Mail and just obliterate your Sent mailbox. Kind of a drastic solution, and will have a bit of collateral damage, but would you rather lose the record of emails you've sent or not be able to use the program at all?
I recently attempted to send an email with many recipients. Some of the addresses were rejected. When the screen popped up to announce this, the red close button was missing from the back screen. I can't edit or do anything with the announcement screen, I can't do anything with the original email screen where the red close button is missing. I can force quit mail but everytime I open mail this frozen screen pops up. Thoughts?

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