Freehand plasma or oxy-acetylene cutting frequently wanders pretty far offcourse, but plasma cutting along a straightedge is a lot more precise. If you want a complicated shape cut out of metal sheet, rather than a straight line, you can cut out some kind of pattern instead of using a straightedge. For plasma cutting you may be able to use laser-cut MDF, but oxy probably needs something that can resist the heat.
Dried mud is quite possibly an adequate material for this, but if not, surely fired-clay ceramic is. You can roll the wet clay body into a plastic sheet, let it dry to leather-hardness to get most of the shrink out, then cut out the desired form with a knife or perhaps a wire. Alternatively, a sheet of gypsum can be either cut to shape or deposited as paste.
How do you know where to cut? You might be able to use a knife plotter like those used to cut vinyl, but a probably-lower-budget alternative is to project the shape to cut onto the surface with a laser, then cut by hand. For small projects, you can print out a plan on a laser or, better, inkjet printer, and glue it onto the pattern before hand-cutting.