How can I export a spreadsheet using the API?

Just as I have the option to go into my deals, click on Everyone, then “export filter results” and finally select a XLS (Excel) file, how can I do the same using the API? How can I get this Excel file from the API?

this API specifically

If the question is still relevant, you can use the 3rd party solution for that assignment.
Take a look at how the service handles Pipedrive to Excel export.