Jason,
Twiggi uses mysql. SME does a complete dump of mysql during a backup. This dump file should be inside the backup file or on your tape. I don't know mysql syntax or administration, but you should be able to restore the dump from any SME backup file. I am guessing every database contained in your mysql is inside the dump file...I have used winrar for windows to open a sme backup to desktop file and extract certain files. You do have to reset the correct ownership and permissions on anything you extract from this file.
Hope that helps,
ryan