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]> dump.sql
This above command exports your database and save it as "dump.sql".
Importing a MySQL db from file:
mysql -h [SERVER] -u [username] -p [dATABASE] <dump.sql
This above command will import your dump file to the database, the will overwrite existing tables with the same name.