Convert STL to SVG With TinkerCAD

You should be able to cut through 0.25" materials. What kind of wood are you using?

I just wanted a cross-section of my shape, but this would also work with layers. I don’t see how you can get around using layers the thickness of your material, though, unless you just make your model really small.

See if this tutorial sheds any light for you: A Cardboard Castle using Free Tools =)