Slicer that exports vectors or pics for every slice
Your approach is one of many and you may find that Slic3r will do as you require.

There's a direct reference to generating SVG files (vector) at this link:
http://manual.slic3r.org/advanced/svg-output

You may have to create a printer profile based on irrational figures when compared to conventional 3d printers. Your 2mm "layer height" should be matched in the printer settings to an appropriate nozzle diameter for the desired result.

You may find also that Simplify3d will create such files, but it's not a free program.

An alternative to 3d printer slicing software would be to use OpenSCAD to import your model (or create it directly in code) and use the Projection command to generate the individual layers. I've done this and found it works well, but the process to learning the necessary code was time consuming, as I'm not a programmer.

You would also want to incorporate some form of registration in your model, cylindrical holes or external tabs to enable you to properly align each cardboard layer.

If you have a makerspace nearby or know someone with a suitably sized laser cutter, you may also save some labor cutting each panel, as the laser will accept the vector files easily.