While there isn't a way to export/download your orders from the Orders section of the Mayple app, you can do this action from Shopify itself.
Below are the steps:
Log in to your Shopify
Go to the Orders section
If you want to export only those orders that are fulfilled by Mayple, you can select the location as "Mayple Fulfillment"
4. Click Export
5. Specify your export preferences.