If your opponent has a standstill on an otherwise empty board, is there a way to remove it without your opponent drawing cards?
You need to look for abilities that can be activated from places other than the 'field, since abilities don't trigger Standstill.
You can cycle Resounding Wave targeting Standstill and a land, as cycling is an activated ability it won't cause Standstill to trigger.
702.28a Cycling is an activated ability that functions only while the card with cycling is in a player’s hand. “Cycling [cost]” means “[Cost], Discard this card: Draw a card.”
Okay, I think I've found another solution.
Since it's your opponent's turn, your trigger goes onto the stack last, and resolves first.Then,
genesis hydra would have to find a notion thief, and it will put that directly onto the battlefield.
At that point, standstill gets sacrificed, and you draw the 3 cards
You can counter it when it is being cast.
If you wanted to ensure that if it triggers it does not get a chance to be sacraficed, then you need to use an ability that wipes the stack like the one found on Sundial Of the Infinite.
Another way would be to destroy it without casting a spell. You could use the ability of a creature already on the battlefield to destroy it after it is played.
Removing a player from the game removes their permanents along with them. Attacking with man lands such as Stirring Wildwood or with tokens from Decree of Justice will either kill the player or pressure them to break standstill themselves. Standstill decks will usually run 2/2 man lands, so having lands bigger than that (such as the 3/4 Wildwood) can win that battle (though do watch out for Wasteland; you will probably need a set of these yourself).
Also, if you have an effect like Boseiju, Who Shelters All (since Standstill decks are usually chalk full of counterspells), you can nullify the effects of standstill with cards like Wit's End or Mind Twist.