How do I stop new submissions on a form?

You can simply disable the form, then it will not be available anymore, this guide will help you: How-to-enable-disable-a-form 

You can also limit the number of submissions that you want to receive in a form, here is the guide that will help you to do that: How-to-limit-submissions-in-a-form

If this does not help you, please let us know and we will be glad to further help you.