Forum:Kycoo Vs Exodia

When Kycoo the Ghost Destroyer makes battle damage when he is battling against another monster, you can remove the destroyed monster?

In a duel, I activated Magician’s Circle, I summoned Kycoo and my opponent summoned a leg of Exodia, I attack and we didn't know who won.

The effect of Kycoo is resolve before or after the destroy monster is send to the graveyard?