@Davi_Matos in Slicer-Liver we do something similar, but I’m not sure you can take advantage from it directly, as it is very oriented to liver resections (one assumption is homogeneous tissue, in your fig3 there seem to be more; one requirement is having both segmentation and surface mesh). There are some discussion on the topic here: Beginner question: liver volumetry - #9 by RuoyanMeng
In my view, it is possible to achieve what you want using 3D Slicer, but you need to develop your own specialized tools for the task. A procedure to do this may look like this:
(1) Place surface markups/bezier surface in 3D space at the desired location.
(2) Create a temporary segmentation (copy) to work the separation
(3) Transfer the surface to image space by evaluating a high-resolution evaluation of if and setting the voxels intersected with a value. This will create a barrier in the segmentation.
(4) Apply a region growing on either of the sides, for this you typically need a seed point, but if your segmentation contains structures which are always on a certain side of the cut, you can use those. This would leave you with a mask that you can use for separation in image space, later you can reconstruct the 3D surface, if needed.
I hope this helps.