How can I clear test data in Stripe via the API?

The Dashboard appears to again have changed for me at least. I don't have the Data section under Compliance & Reporting, however in their search menu if you type "Data" and then select the "Developer" option that appears, that page will give you the option to remove the data.

The dashboard has changed once again. You can now find it by clicking "Settings" in the lower left-hand corner. Then scroll down to the "Compliance and reporting" section. Click Data. Here you will find the "Delete all test data..." button

No, it isn't possible to clean all test data via the API -- only via the dashboard. Sorry!

In the Dashboard, the option now lives at the bottom of the Developers page

In the latest update of stripe you can find the action button for removing test data in

https://dashboard.stripe.com/test/developers