Does a man's pronouncement of "You are divorced" to his wife count as a divorce if he said it believing she requested it by saying "throw it," while she actually meant "throw the card," given that this is the second pronouncement and they had intercourse afterward?

Divorce does not take effect unless its wording is attributed to the wife. If it is not attributed to her, then it is a kinayah (allusion) and refers back to the husband's intention. Should he have intended divorce, then it takes effect, and its occurrence is not prevented by the wife's intention to throw the card, not to be divorced, for what is considered in this matter is the husband's intention.