Against to what most people thinks (included mexicans) its not related to the fear that many people have to clowns.
It comes from the rodeos entretainment, when the cowboys rides the bulls and can't hold any more, the danger to be killed by the bull once the cowboy falls to the ground it's extremely high, specially 'cos the falling hurts a lot and many times the cowboys can't stand up and of course, unable to scape to safty. To avoid this, there were born the Clown Cowboys or Clownboys: Clowns which porpouse wasn't really to just entertain the spectators but to taunt and pull bull's attention away while another Clown carries the aching and beaten cowboy.
So then, when the Clowns carries you was only at the last point when you were completely beaten and unable to even stand up and run for your own life.
"Ya te cargó el payaso" is an expresion for any situation where you are in such and inminent "huge" problem and yes, you are F%$