The paper said it would split the money, estimated at around £50,000, between the Red Cross and an armed forces charity.
But after private discussions with Mirror executives, the charity's chief executive, Sir Nicholas Young, decided it would "not be appropriate" to accept the money.
The paper has not yet decided how to distribute the funds.
Also last week, the Red Cross appointed seven new trustees as part of its drive to become a more democratic, transparent and diverse organisation.
It now has 16 trustees in total.
The charity's secretary, Michael Evans, said the organisation had set itself two targets in terms of trustee representation - for its elected board membership to be "more democratic and transparent", and to "move away from the traditional profile of the typical member".
Evans said the typical member was a branch president, and "while we don't want to exclude them, we do want to make it easier for grass-roots volunteers to get on the board".
He cited Dr Marcus Stephan, chief executive of the British Society of Immunology, as one of a number of those that met these criteria among the latest intake of new appointees.
Four of the new trustees are elected members, the other three co-opted, meaning they "traditionally come from positions of high standing, such as finance directors or ambassadors, and are often retired".
Evans added that the Red Cross had recently vowed to "address the lack of diversity in both the society and the board, which is not an easy nut to crack".
However, with the appointment of Dr Ahmed Hassamm, managing director of Quest Vitamins, to the board, Evans believed the organisation had made a good start.
The new trustees have joined as a result of natural rotation. Each can serve up to six years and must step down for one year before standing again.