While facing an opposing dragon, and while having both a fallen elf in play with enough life quantum to play his mutation ability, and also while having an electrum hourglass in play with enough time quantum to play its hasten ability, I clicked on the hourglass to play hasten and clicked on the fallen elf to play mutation very close together.
The game reacted by starting the card drawing animation and also by placing the target sight icon on all creatures in play and popping up the 'select a target/cancel' message box. As the card drawing animation proceeded, the target sight icons disappeared, thought the message box remained. Once the animation finished, any creature I clicked would not mutate, and eventually I clicked cancel to dismiss the message box.
I might expect the game to have kept up with the speed of clicking so that both the mutation and the hasten abilities would have executed without problem. Although as well I don't really need to be clicking that superfast either.