You can work out with Time Machine to exclude all the other folders except your Apple Mail Database Folder. As you haven't mentioned which version of Apple Mail you are using so here is how you can find your Mail Database Folder:
Find and Open the Folder Where OS X Mail Stores Mail
To go to the folder that holds your OS X Mail messages:
Open a new window in OS X Finder.
Select Go | Go to Folder… from the menu.
You can also press Command-Shift-G.
Type "~/Library/Mail/V3".
Press Enter.
You can find your folders and messages in sub-folders to the V3 folder:
Local mailboxes are in the Mailboxes sub-folder.
POP email accounts can be found in sub-folders with POP- in their name.
IMAP accounts' mailboxes are in sub-folder that have IMAP- in their name.
The messages are stored in .mbox folders, one per OS X Mail email folder. Open and explore these folders to discover (and open or copy) the emails saved as .emlx files.
Find and Open the Folder Where Mac OS X Mail 5–8 Store Mail
To open the folder where Mac OS X Mail keeps your messages:
Open a Finder window.
Select Go | Go to Folder… from the menu.
Type "~/Library/Mail/V2".
You can have Finder auto-complete the folder names by pressing Tab.
Click OK.
Mac OS X Mail stores the mailboxes in sub-folders to the Mail directory, one sub-folder per account. POP accounts start with POP-, IMAP accounts with IMAP-.
Find and Open the Folder Where Mac OS X Mail 1-4 Store Mail
To locate the folder where Mac OS X Mail 1-4 stores mail:
Open a new Finder window.
Go to your home directory.
You can use the Home toolbar button or
select Go | Home from the menu to go home.
Open the Library/Mail directory.
Also there are multiple application available online for mac database backup as mentioned by Eric in the above post. There is one that is specifically for emails only and backs up all the email clients on Mac. Have a look: http://www.mailbackupx.com/how-to-scenerios/how-to-backup-apple-mac-mail-mails-o n-mac.html
