How to move all of my mails to external HD and make them appear only when its connected
Confirming your requirement.

You want to remove all (or specific account) emails (from mail.app) from your hard drive and move them to a external drive. (this is not to have a copy of your emails on the hard drive).

Than you want the Mail.app to use that external drive from now on as email database.

One way to accomplish this is as follows:

It is called symbolic link. What it does is you create a link in your mail so it looks for your emails on the external drive.

Step 1: Find the file you need to move and move it.
The Mail files are stored in /Users//Mail and /Users//Mail Downloads. To get to these files, open a new finder window and press Command+Shift+G and type “/Users/(YOU)/Library/” . This takes you to the Library folder, where you’ll see both Mail and Mail Downloads. Grab both of those files and move them to your external drive.

Step 2: Delete the files you moved from the Library folder. (if you worry about deleting then just move to desktop for now). In other words, make it so that the files do NOT exist in your Library folder, but they DO exist on your external drive.

Step 3: Create a Symbolic Link to the folders on the external drive.
Download the SymbolicLinker App and install it by clicking the “SymbolicLinker.service” file within the DMG file. Once installed, you can then go to the files on the external drive, right click and select “Make Symbolic Link” at the very bottom of the menu. This will create a folder right next to the actual folder.

Step 4: Move the Symbolic links to the Library folder. If you’ve already closed the Library folder window, re-open with the instructions from Step 1. Once open, drag the symlink files on the external hard drive that you created in Step 3, over to the Library folder. Once they’re both in the library folder rename them so they have the EXACT same name as the actual files did (in other words, remove the “symlink” at the end of the file name).

If you’ve followed all the steps you should now have links in the Library folder that point to the actual folders that are now on the external drive. From here on, it’d probably be a bad idea to rename your external drive. You might be able to without it breaking, but it doesn’t sound like it’d be a good idea (test first). Also, if the external drive isn’t mounted on the OS (it’s not plugged in) then you’ll be unable to open Mail (since the files for Mail are on the external drive now). 

Copyright 2003-2011 Nick Zitzmann.