When jousting, are minions drawn from your full deck or just the remainder?

In a joust, each player has a random minion drawn from their deck for them and the mana cost of each compared to find a winner.

However, I'm curious to know if the draw pool for these cards is the full, original deck or just the cards left at the point the joust starts.

Or to put it another way: if my deck contains two copies of a minion and I've drawn and played them both during a game, can they be drawn again in the event of a joust?

Jousting only occurs with minions left in your deck, not cards already drawn.

To use your example, since you've already played the cards, they cannot be randomly picked from your remaining deck so they would not be part of a joust.