archive mail to external drive, delete on computer's drive

I've spent the last two hours trying to understand how Mail is set up and I'm getting nowhere. My Mail library is too large, and my iMac's solid state drive is too small. I'd like to archive some old email onto an external hard drive, then delete those emails on my solid state drive to reduce the mail library size (and not have them sync back onto my hard drive after deleting them). Ideally, accessing the mails in the archive wouldn't be too painful, as I have to search for old emails regularly.

I'm running Mountain Lion, getting ready to upgrade to Mavericks (thus the need for more disk space). My email accounts are set up as IMAP, and are mostly Gmail accounts, and Mac Mail is my only email client.

I made a Smart Folder in Mail for old emails, and Exported it to an external drive. While something got written on the external drive, I'm pretty sure it wasn't the emails I want to export/archive because the files I saw created weren't big enough. [Correction: since I wrote this, the file size has grown, so perhaps Mail wasn't done exporting. If this is all I need to do, how do I now delete the emails from my iMac and the Gmail server? And how do I open the archive when I need to search it? Right-click to Open File with the export doesn't do anything, perhaps because I haven't deleted anything yet.]

As I understand it, "Archiving" within Mac Mail just removes mails from the Inbox and puts them elsewhere on the same drive, and wouldn't reduce my library size. I did try to create a new Mailbox on an external drive, with the idea of dragging items into it for archiving, but the dialog box for selecting the location of the Mailbox only gives local options, nothing external.

This seems like a really basic question, but I honestly cannot figure out how to do this after a lot of looking around. I saw too many answers involving Terminal, which gives me pause. If there is any good overview of how Mail works, I'd welcome that too, because Help within Mail was NOT helpful.