Can I mill an opponent who has Emrakul, the Aeons Torn by comboing until opponent's deck is stacked in an exact way?
You are not allowed to execute this entire combo, either using a shortcut or playing it out explicitly.

You cannot execute this combo with a shortcut because of the way shortcuts are defined in rule 720.2a of the Taking Shortcuts rules section:


  At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can't include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.


In the combo you describe, you determine whether to continue or stop based on which cards, and how many, are still in the deck. That in turn depends on when exactly the Emrakuls got milled and their abilities triggered, which means that your actions would fundamentally depend on those game events, making this an invalid shortcut. You can see a ruling here about a different combo that also involves an indeterminate amount of shuffling.

You also cannot execute this combo without using a shortcut. A fundamentally identical combo exists in the deck Four Horsemen, which involves milling its own library including Emrakul in order to eventually end up with a particular sequence of cards in the graveyard and the library. Previous rulings have established that this combo is slow play and it should not be played in tournaments. The basic reason for this is that the combo can take unbounded time to complete, and every time you shuffle Emrakul in you are starting all over without making any meaningful progress.