We see Slayer stalking and spying others several times in the series. He would spy on Asmo in the real world, see that he apparently goes in a certain deserted direction and then jump there via TAR to surprise & quickly kill him with a fast weapon (like a crossbow). If Asmo hadn't opened the door, Slayer had simply waited for another good opportunity.

And as said, if a Forsaken patron orders Slayer to take the body so that Rand won't find it, he would certainly do it. Slayer even killed a Gray Man, who attacked the Wondergirls in the WT, apparently because he was ordered to do it. Besides, Slayer could still butcher Asmo's corpse a bit more in TAR, if he wanted to.