Normally a war machine requires a full crew to work it properly - to carry ammunition, push the machine round to bear on its target, and so on.
If members of the crew are slain, this will affect the movement rate of the machine as described above, but will not slow its rate of fire until there is only one crewman left. The last crewman left will then be unable to cope - the machine can be fired normally one last time, but from then on it will have to miss a whole turn (for the remaining crewman to reload it) before it can shoot again, This is in addition to any penalty imposed by a misfire result. Obviously, the machine requires at least one crewman to work, so the machine will become useless should all of its crew be slain.
Some war machines, such as the bolt throwers made by the Elves, are smaller and much easier to operate than the larger, more cumbersome ones. If a war machine has a crew of only two models from the beginning of the game (as specified in their entry in the appropriate Army book), they can be operated by a single crewman. If one of the crewmen of this machine is slain, the remaining one can therefore keep firing without slowing down the machine's rate of fire.