Can I delete submissions?

Yes, you can. Here's our guide on how you can do that in a form: https://www.jotform.com/help/377-How-to-Delete-Form-Submission-Data. 

Please note that once you delete the submissions, there is no way you can recover them later so we can suggest keeping a backup by getting the excel file.

https://www.jotform.com/help/44-How-to-Export-Form-Data-to-Excel