Unless you want to modify a mesh dynamically (that is at run time, in a way that is different each time). The you should edit your mesh in a proper editing tool. Like blender. jME is a game engine not a modeling tool.
Then even if you still want to do this, (which i don't recommend), you need to be able to understand polygons and the data structures that represents them in opengl. This is typically indexed vertex buffers. Now you need to know your basic vector math to do things like work out where a cutting plane cuts a poly, add the required vertexs and triangulate the now not triangle triangles. And of course as is typical with this type of coding, deal with all the degenerate and edge cases.
But really, no matter what game engine you use. It is always better to mesh manipulate in a proper modeling program.