I want to hide a submit button from the users

I've set up an approval form.  There is a hidden section at the bottom of the form for the approving/denying a request.  There is a submit button that depending on if it's accepted or denied, sends out an email to either our help desk or back to the user.  I want to hide this submit button from the user but have it visible when approving the request.

Based on what you have explained, seems  like the original submission is sent to someone for review, then once the submission is reviewed, the form is submitted again. 

If this is the case, then you will need to conditionally hide the fields based on the submission status, you can know if the submission is being edited using the Get Form Page URL widget: https://widgets.jotform.com/widget/get_form_page_url 

How-to-Add-a-Widget-to-your-Form

This guide will help you setting up the conditions to show/hide the fields (including the submit button): How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

Hope this helps.