The operation of the fuel selector to stop the fuel flow is something I check during post maintenance testing - for exactly this reason. If the fuel cut off will not cut off (and I had one once), you also could not starve an engine fire. Yes, for carburetted engines, the engine must burn out the contents of the carburettor fuel bowl. If you need to shut down the engine with the fuel valve, run the engine at a higher RPM, it'll use up the fuel more quickly. If you're flying a plane which has the failure of a mixture control, the failure of both mag switches, and a fuel valve which will not turn off the fuel, well.... it's not airworthy. Sure, a mixture cable can break in a moment. But you should have done a live mag check preflight, and not taken off if you cannot mag switch off the engine (plus it's unsafe when it's parked). Few carburetted engines do not have an accelerator pump. If it lacks one, yeah, jamming the throttle will make it quit. Try it, nothing to lose.
So, mixture has not control, mag switches are failed, fuel valve will not stop the fuel flow.... Turn the tail into the wind, Carb heat on ('cause it reduces the RPM a little), open the throttle somewhat, and try to select the CS prop to full coarse (depending upon the prop design, it might go coarse and stay there), turn on everything electrical (the alternator creates torque proportional to draw), and select throttle to idle (reduce torque to a minimum). Maybe the engine [at idle] torque will be so low that the engine will stop under the added load.
If it's an injected engine, operating the electric fuel pump, particularly at high speed, while the engine is at slow idle, 'might make it quit by flooding it (it did on the C 310 I used to fly
).
If not, you're either going to have to sit in it until it runs out of gas. If you can't wait, and are willing to damage the engine to stop it, spray lots of water into the air intake. Not a good ideas, but it sounds like you have an emergency - you gotta do something!