Emrakul, the World Anew

If you discard a card with madness while a spell or ability is resolving, it moves immediately to exile. Continue resolving that spell or ability, noting that the card you discarded is not in your graveyard at this time. Its madness triggered ability will be placed onto the stack once that spell or ability has completely resolved.

Emrakul, the World Anew's triggered ability will resolve before Emrakul does. If Emrakul is countered or otherwise leaves the stack in response to that triggered ability, the triggered ability will still resolve as normal.

Cards are discarded in a Magic game only from a player's hand. Effects that put cards into a player's graveyard from anywhere else do not cause those cards to be discarded.