Something that none of the other answers have brought up so far is that mill already has an established technical meaning in certain subsets of the gaming community.
In the trading card game Magic: The Gathering, the verb mill is defined to mean "to place that many cards from the top of a player's deck into the graveyard [a discard zone]". This is defined in 701.13 of the Magic: The Gathering comprehensive rules.
For a player to mill a number of cards, that player puts that many cards from the top of their library into their graveyard.
For someone unaccustomed to the Magic subculture, mill might seem like an unusual name for this effect. It derives from the card Millstone, an early card printed with this effect. In fact, the rules text of the latest printing of Millstone shows how this word is used in this gaming context:
Target player mills two cards.
Because Magic has an outsized influence on the trading-card game genre as one of the first (and one of the most popular) trading-card games, the term mill has found usage in other trading-card game communities for analogous effects.
For example, a "Mill Rogue" deck in the game Hearthstone is built around forcing the player's opponent to draw too many cards from their deck, thus wasting the extra cards. The entry for "mill" on the Hearthstone wiki even acknowledges the origins of the term in Magic:
Milling itself is a trope imported from Magic the Gathering (MTG) to Hearthstone (HS) vocabulary. The trope namer, Millstone, was the first card in MTG to feature the mechanic of directly removing cards from decks.
Similarly, Yu-Gi-Oh also has the concept of "Mill Decks", again attributing the concept to Magic:
The name "Mill Deck" comes from Millstone, a card in the first widely-popular TCG, Magic the Gathering.
In summary the word mill has a very strongly established technical meaning in at least one gaming genre. Using this word in a different way might lead to confusion if the people you are talking to also happen to be card-game players and are familiar with this specific usage of the word!