Last Man Standing (also LMS) is a game mode the community came up with. It is comparable to Sumo, players have to push each other off a platform, optionally with the use of Pick-Ups.
Usually, LMS is played in the Single Race mode in multiplayer. Battle Tag mode works as well, however, some levels are not designed for the jumps that you can perform in this mode. The host needs to launch the game with some arena levels installed.
The host of the game specifies what cars are allowed to use. For smaller arenas, heavier cars could be chosen, while on larger arenas, heavy cars could make the game more boring.
It's generally advisable to play with lighter cars so rounds don't last so long. To make it even more interesting, the host can choose Simulation Mode.
Contenders who fall off the platform usually have to wait for the host to restart the game/round.
Currently, there is no way of checking the order in which the cars fall of the platform.