How to copy a database from server A to server B:
(Assumes database name is the same on both servers.)
On server A:
backup_mysql_db $dbName > /tmp/$dbName.sql
On local:
scp A:/tmp/$dbName.sql B:/tmp
On server B:
mysql -uroot -p < /tmp/$dbName.sql
If any modifications are needed, they would be run on server B at this point.