When Cyclopean Mummy dies, exile it.
10/4/2004 The Mummy does go to the graveyard and trigger abilities which watch for something going to the graveyard. It then gets exiled as a triggered ability.
10/4/2004 It does not get exiled if it goes to the graveyard from someplace other than the battlefield. This includes discarding from your hand or if the spell is countered.