Exporting the entire process from an existing Team Project is probably impossible to be honest. You can get a part of the contents like the work item type definitions and source control settings, but things like reports and SharePoint template can't just be "extracted" again out of the Team Project. The process template is really just a script to set up a new Team Project, it's really not intended to extract such a script back out of an existing project.
The recommended approach is really to keep your original Process Template in source control, and while you make the necessary changes to it (and check them in to source control again) upload the modified work item type definitions and other customizations to live Team Projects as needed. But I would always keep the source controlled template as the single true version.
The recommended approach is really to keep your original Process Template in source control, and while you make the necessary changes to it (and check them in to source control again) upload the modified work item type definitions and other customizations to live Team Projects as needed. But I would always keep the source controlled template as the single true version.