Yes, this was addressed in another thread (or possibly the FAQ). If it's in a halo, you can't play it.
I would add the caveat "with that same group of saints."
As long as you are doing something like using the companion app to track cards, then there is no reason why you couldn't unslot the mission fragment and use it to play with another group, and then add it back to the original saint's halo before your next session with the first group.
I have done this once or twice, since I had some friends I wanted to introduce to the game using Taking the Plunge, which was already completed and slotted by someone in my main weekly group.