No. There's probably a better than 50% chance that I wouldn't even like the random stranger. Also if I cut off my own limb, the chance of me dying is extremely high. Firstly, I'm in an extremely vulnerable state (in the presence of a sadistic psychopath no less), almost certainly passed out. Even if he's good to his word, I would need immeadiate medical attention as I would be suffering from massive blood loss (minutes to live at most). Assuming I survive that the risk of infection (and subsequent painful death) is very very high.
To be honest even if I wanted to (which I would'nt) I don't think I could physically saw through a limb without survival instinct adrenaline boost kicking in, lopping something off quickly yes, but sawing no.