1) to do something automatically, without thinking, because you are an idiot.
2) to do something quickly and appear to be an idiot because you didn't think beforehand. Possible when reacting by reflex or when startled.
3) (archaic) to use a catch-phrase or cliche in a really stupid way because you are an idiot. Similar to "idiomatically," but with a lower IQ.
1) Hey, good job, moron, you idiotimatically left the cardboard under the this frozen pizza when you put it in the oven.
2) So Joe jumped out from behind those bushes last night and scared the crap out of me; I idiotimatically tried to hit him with the half-empty case of beer I was carrying, scattered beer cans all over the street.
3) "That's what she said."