Use vtkImageActor::SetDisplayExtent
to display a slice of the image data.
For example: (From https://examples.vtk.org/site/Cxx/ImageProcessing/EnhanceEdges/)
originalActor->SetDisplayExtent(
reader->GetDataExtent()[0], reader->GetDataExtent()[1],
reader->GetDataExtent()[2], reader->GetDataExtent()[3], middleSlice,
middleSlice);