I have a Process StartForm with a mandatory field. By default, the validation is

What version are you on? In 7.4, if this is a SAIL form you can achieve this. Check out the SAIL recipes in documentation.
Other points, if a start form, you don't need a cancel, as the user can navigate away without starting process. Non-SAIL form, you will need to not mark as required and check using gateway if value entered and submit clicked.
Hope that helps!

You can do 1 thing to handle this: Do not make that field required but just put an asterik on Field label. And on Submit button, check if that field's value is null than divert the flow to the form and enable show an Error message through enabling a boolean variable. In this way you can skip the validation on Cancel button.

you can use advanced form utilities to do this.

if you are using sail forms for this. add "skipValidation=true" to the button compoonent