If I respond to {Emrakul} hitting the graveyard and use a {Surgical Extraction}, that's legal right? Emmy has protection from colored spells but while he's in the graveyard that doesn't matter, correct?
Yes, Emrakual's shuffle ability goes in the stack and then Surgical Extraction is played and it resolves before his ability. So yes it works
Keep in mind Emrakul's ability will still resolve, and though he will be exiled the GY will still be shuffled into the library.
The real question was if I could target him while he was in the graveyard. Which has been answered. Thanks all.