There is no way to stop SQL Azure Database to avoid billing charges when not in use. The azure virtual machine can be suspended and by doing that you can avoid hourly charges, but you cannot do the same with a SQL Azure Database which is charged hourly per database.
There are few alternatives to reduce or stop charges:
The pricing tier of SQL Azure Database can be changed to Basic.
Export the SQL Azure Database to Azure storage and then delete the SQL Azure Database and restore it when needed.
Delete your SQL Azure Database and later use point-in-time restore to restore your database depending on the pricing tier associated with the database. Databases with Basic pricing tier can be restored within 7 days after deleting it, while the retention period for Standard is 14 days and for the Premium pricing tier is currently 35 days.
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