Help creating sections of a OBJ in Rhino for Mac

Im very new to Rhino and to CAD software in general. In the past I’ve used Fusion to create solid sections from a mesh. My goal is to make a “3d puzzle” off of a OBJ to then be able to CNC router it out of plywood to assemble. Ive tried to use CONTOUR to create sections but they don’t create a new layer for each so its un manageable, help with that itself would be huge. TIA!

Why is this unmanageable? Can you post a file with just a few of these so we can see what you are shooting for?