Printing PCBs using conductive paint?
Cutting a stencil as you suggest is not a viable option. The main reason is that for almost any circuit there are parts of your stencil that will fall away as you pick it up from the cutting board and try to transfer it to the circuit board medium. The simplest way to describe the problem is to consider a similar application with a font stencil where the parts inside letters like B, D and P will fall out.

Conductive inking is done on some materials like the clear plastic sheets that you will find inside the typical cheap computer keyboard. But the typical applications of such are relatively high impedance circuits with low current flow. The typical conductive inks are also not normally particularly solderable and even if tried will melt or burn the carrier medium.