If I have the Starter account, can I save the data from a submitted form then delete it, so it is not going toward my storage?

Yes, you can clear your storage space by deleting the submissions with the uploaded files. Here's a guide: How-to-Delete-Form-Submission-Data.

We do have an app called Auto-Delete Submissions. This app deletes new form submissions instantly as soon as they are received. Here's the link: http://auto-delete.jotform.io/.

Related guide: Understanding-Your-Account-Usage-and-Limits

Hope that helps. Thank you.l