Hello,

You can simply use the mysqldump command via ssh in order to export your databases and then copy them anywhere else (either locally or to other server) using scp or rsync.

The command will look like this:

mysqldump -u [username] -p [database-you-want-to-dump] > [path-to-place-data-dump]

So it could be something like this:

mysqldump -u root -p mydatabase > /home/myuser/database-dump.sql

You can check this article as well, because everything is explained in details:

https://www.digitalocean.com/community/tutorials/how-to-import-and-export-databases-in-mysql-or-mariadb

Let me know if you have any questions.