It doesn't make any sense why....
They would cut his finger off first thing does it?
I mean I get that it's obviously to raise the stakes for their situation, but think about this from a real life point of view, if you kidnapped him would you really want to first thing, without even talking to him, cut his damn finger off, giving him a perfect reason to be pissed off and want to kill you?
For all they knew when they told Charlie the situation he might be "sure, I'll help you out" or he might not be happy, but if you succeeded and let him go unscathed no harm no foul he'd have no good reason to want to kill you.
It seems like you wouldn't cut his finger off unless he was being uncooperative, I mean they don't even give the finger to anybody as a threat making the whole thing pointless.
This is an alright movie, but certainly not a great one.