I would have to spend a bit of time thinking, and then we'd probably fall and die.
But what I'd probably do is tell my friend about the situation, and ask him if I should cut the rope, explaining to him that if I don't, we both die. If he says yes, I'll do it, but definately hesitant of doing so. If he says no, we both die, right before I speak to him for the last time of my life.