You can export your DB with SMMS and restore it to another server/new DB if this is one time task.
You can also take frequest backups and store them to azure storage account as .bak and restore from them.
You can use an automation runbook/powershell script similar to one given here :
https://www.powershellgallery.com/packages/Backup-SQLAzureDb/0.2.0
If both the DBs are on Azure SQL you can copy using simple powershell command directlay to new server
New-AzSqlDatabaseCopy -ResourceGroupName "<resourceGroup>" -ServerName $sourceserver -DatabaseName "<databaseName>" `
-CopyResourceGroupName "myResourceGroup" -CopyServerName $targetserver -CopyDatabaseName "CopyOfMySampleDatabase"
New-AzSqlDatabaseCopy -ResourceGroupName "<resourceGroup>" -ServerName $sourceserver -DatabaseName "<databaseName>" `
-CopyResourceGroupName "myResourceGroup" -CopyServerName $targetserver -CopyDatabaseName "CopyOfMySampleDatabase"
Or use a copy of TSQL command :
CREATE DATABASE Database2 AS COPY OF server1.Database1;
Details Here