Mac Mail filling up?

I have over 10,000 emails in Mail in various folders. Is there a limit to how many I can store / keep? And is there a way to "move" them to an external HD and clean up Mail? I have Time Machine running on an external HD so I know they are being backed up there.

There are several applications out there that can do this though I have never tried them. I think some of them essentially create a searchable database. Here's one example.

You can also perform an archive from within Mail

And there's also this: https://itunes.apple.com/ca/app/email-archiver/id407821589?mt=12

Pricey, but wait till its on sale. Works well.