Copy SQL Azure Database to different Server
Although this question is very old, it's the one I came across when trying to find out if I could easily copy an Azure SQL database from one server to another.
It turns out that it's now as simple as navigating to the source database from http://portal.azure.com then clicking copy and choosing the new destination server.
The whole process is explained in more detail in this article:https://azure.microsoft.com/en-us/documentation/articles/sql-database-copy/
To execute DB copy between 2 different servers you must be connected to the master database of the destination SQL Azure server and have correct permissions.
The exact same login/password must exist on the source server and destination server and the login must have
db_owner permissions on the source server and
dbmanager on the destination server.
Read more about it here: http://msdn.microsoft.com/en-us/library/ff951624.aspx