SSH is very good at both import and export MySQL databases with MySQL command, so you can do both :
Export a MySQL db to file:
mysqldump -h [ SERVER ] -u [username] -p [ DATABASE ]> dumpfil.sql
This command exports your database and save it as " dumpfil.sql "
Importing a MySQL db from file :
mysql -h [ SERVER ] -u [username] -p [ DATABASE ] < dumpfil.sql
This command will import your dump file to the database , it will overwrite the existing tables with the same name