You can push it via a CLI ftp command to another ftp server from ssh.
What ya need to do is backup to a folder you can access with ftp and grab it that way to download.
Say you have cpanel with a user named joeblow.
mysqldump --opt -Q -u dbusername -p databasename > /home/joeblow/backupname.sql
when done, joeblow hits ftp and the file is right there safe above public_html.
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