It’s a little known fact that the British carried out extensive testing of potato-based anti-tank warfare during the early days of WWII and found that it was almost frighteningly effective. Potato pluggers had to retire smartly after insertion of the vegetable to avoid being hit by shrapnel from the over-pressurized tank.
However, those crafty Britishers let the Germans capture spies carrying an altered version of the testing reports which falsely stated that the potato-in-exhaust technique had proved to be a failure. As a consequence, the German Kartoffel Barriere Entwicklungskorps was disbanded as superfluous, which probably cost the Germans the war. The British ruse of misinformation spreading was so successful that even to this day, people laugh at the effectiveness of spuds in defeating heavy armored vehicles.
Of course, the real tragedy of the war was the British abandonment of the classic Lee-Enfield-Pentland-Squires bolt action in favor of the newpotatoesfangled automatic weapons.
My wife once turned our car around on a narrow dirt road, and in the process, backed the rear end up against an embankment, tail-pipe foremost. The engine cut our within a couple of seconds, as soon as the exhaust was blocked. The engine would restart, but cut out again immediately. I had to get out and rock the car forward, creating a separation between the tailipipe and the embankment, before the car would run long enough to pull it forward under its own power.
That’s only because the engine lacked the ability to pressurize the exhaust system to eject the entire embankment.
A plug of mud, as you noted, was not obstacle. The entire Earth* was.
*Technically, since the embankment was part of the surface soil, which was attached to the subsoil, which was attached to bedrock, etc. You were trying to shoot the entire planet out of the tailpipe. Ballsy, but foredoomed to fail.
ETA: And jtur88 discloses the only way to stop a King Tiger’s engine with a potato: make sure the potato is still fully buried. Because not even a heavy tank has enough horsepower to eject the Earth from its exhaust system.
I offered my anecdote not for the purpose of illustrating some parity between a potato and a solid-state astronomical planet, but to indicate the immediacy of a standard automobile engine failure resulting from the full blockage of the exhaust.
On a serious note, the Brits invented Caccolube, an abrasive that would destroy an engine if slipped into the gas tank. Good luck doing that, but if you’re close enough to try the potato…
A myth about WWII tanks was that most were diesel, and the Sherman was the sorry exception, full of gasoline set to light it up like a Ronson. In fact, of the most-used medium and heavy tanks of the war, only the T-34 was diesel. The rest, German and Brit, as well as the US, were powered by gasoline. The Brits were justifiably fond of the Rolls-Royce Meteor, based on the Merlin.
From reading about the King Tigers, it would be difficult to tell if the engine stopped because a banana, er, potato was jammed in the tailpipe, or if one of about 10,000 other parts just coincidentally broke at the same time.