Drag knife is what a vinyl cutting plotter uses, but material thickness is fractions of mm up to a couple mm mebbe thick, blade just turns around on bearings in its holder, Z is solenoid up / down.
Though plotter makers seem to have no problem with high res USB to stepper interfaces.....

For things with some thickness like foamcore and correx, its CNC with an oscillating knife , drag knife wont go to multiple mm in stiffer materials, which is partly where I started looking at CNC

COMAGRAV oscillating tangential knife

For the sort of cash for a drag knife gadget, if you want to cut vinyl not far off a whole cheap plotter for similar cash.