What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
At JotForm, we want to make sure that you’re getting the online form builder help that you need. Our friendly customer support team is available 24/7.
We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
No, there is no a way to save different versions of your form, at least using a button "Save As", you can clone your forms and have different versions, make changes on each one and you will find them in "My Forms" section, this guide will help you to cloned an existing form from your account: http://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account.
However, I will escalate this as a feature request so our developers will take it into account and depending on the amount of users requesting the same then it may be developed, if it is, we will let you know via this thread.
JotForm Support Manager
Besides to what Keving has indicated, you can also use the Revision History, in case you would like the form to turn back to a previous version,