Apologies for the misunderstanding.
I understood that your current situation is that you would like to take a backup and delete the resources of the RG.
Backup of Cosmos DB database is not exportable/movable, you will need to extract your data using a mechanism like adf/spark to remote location of your choice.
https://learn.microsoft.com/en-us/azure/data-factory/connector-mongodb?tabs=data-factory
Please let me know if this helps by commenting below.
Regards,
Oury