I've came across stunts with Tesla X towing huge weight: over 100 tons of muck and even a Boeing Dreamliner jet. I haven't found any clue as to one or the other video being rigged, so I assume the vehicle is capable of pulling an order of magnitude heavier loads than it's rated for (about 2,5 tons). In both cases the car towed the weight outside traffic, very slowly and over a very short distance.
I haven't looked much into traditional internal combustion cars pulling off such a stunt, but I imagine that both dry clutch and a torque converter will be seriously overloaded in such scenario. A burned clutch disk, as it appears to me, will be the worst damage one could do (stalling the engine for a few times before giving up being more likely).
But what permanent damage could I cause if I took a new production Tesla X or other high-spec EV without any modification and tried something like this myself? Would I risk overheating the motors, reducing battery capacity, warping the body of the car?
Added to clarify: Given the torque available, it seems much easier to tow or pull heavy loads with a standard, unmodified EV than with a conventional car. Failure modes caused by overloading the drivetrain are to a great extent popular knowledge, which is not the case with EVs. How does traction overload affect an EV? I'm interested in both short and long term effects of both one off and repeated overload.
Example answer for a manual transmission petrol engine car would be burned clutch, perhaps worn out transmission or differential gearing.