Can I turn off editing after a form has been submitted?

I want to lock off the editing option when a form is submitted, so that none of the form details can be tampered with

You should make sure that your users do not get the edit link, you may remove such info from your emails, this guide will help you editing the email template: https://www.jotform.com/help/430-How-to-Edit-the-Email-Template-for-Notifications-and-Autoresponders 

Once the edit link is removed from emails, the user should not be able to edit the submission, the only way to do it would be through the submissions page of your form. 

If you have questions, let us know. 

Is there any way to turn off editing through the submissions page? Once a form is filled out we don't want to be able to change any of the details provided to us

There is no option to disable the edit feature in the submission page. However, the submission page can only be viewed by you or edit the submission by your account.

If you have further questions, let us know.