Given Microsoft is deprecating the previous method of exporting a SQL DB they have put up a suggested example here:
$subscriptionId = \"YOUR AZURE SUBSCRIPT
The PowerShell script example in your question above is tested working as expected for me.
However, I am not able to reproduce the same error message as yours even try to use non-existent resource group, database server or database.
Important Note:
$serverAdmin and $serverPassword, their values should be single-quoted instead of double-quoted for the script to workAzureRm.Sql module. Mine tested working is 2.5.0New-AzureRmSqlDatabaseExport command line to see the details