Stopping SQL Azure DB when not in use

As of 22nd September, 2021, The answer is No.

They won't allow it. So the billing will continue for your Azure Database starting the day you create it. There really is no way to pause / stop billing for your Azure SQL Database.

Official Source: feedback.azure.com Please add ability to temporarily turn off/on SQL Azure server to pause billing

Microsoft's official answer appears to be "Yes, you can export your database. Delete the Azure SQL database and that will pause billing. Then when you need it you can create a new database and import your previously expored DB."

I don't believe this is acceptable as an answer for "Allow me to temporarily turn off SQL Server to save on my billing"

This is not an option today - the only choice you have is to reduce the size of the Azure SQL Database which will reduce the cost from the next hour of service. If you really don't want to pay for the DB you could backup the DB to blob storage, delete the database and then restore when required. You could orchestrate this using PowerShell or similar.

Update May 2019: There is a new Azure SQL Database "Serverless" tier coming that might meet some of the requirements around reducing costs by not billing when not in use. Official documentation is available to read.

The databases get backed up automatically just before a drop. so, you can just drop it when you dont need it and restore it when needed.Restores will take some time depending on the database size and how much log you generated, so it wont be fast for large databases.

Also, there is an expiration policy on how long the backups are retained (depends on the service tier) so just watch out for that.

https://msdn.microsoft.com/en-us/library/azure/jj650016.aspx