You need to create a mesh by running the Slice (vtkCutter + vtkPlane) filter rather than a mapper that will extract a slice from the original Volume for at the rendering level.
Can you please elaborate on your solution? If you can add a pseudo-code to your answer it will be great!
Thank you very much for your response!
There is a limitation for vtkOBJExporter: it only works with vtkActor. It does not work with vtkImageSlice or vtkVolume or vtkTextActor. The same is true for all of the VTK exporters, as far as I understand.