You might want to check out Boolean Operation on models.
Eg. in blender getting a “slice” of an 3d model is as simple as applying a boolean modifier. There are many videos about this on youtube: Tutorial: The Boolean Modifier in Blender - YouTube
Regarding jme3, I have found this thread that mentions them: BoolMesh.java (boolean operations on mesh)
If you are not familiar with the concept of boolean operations, I would suggest trying it first in Blender.