how would you know if your finger was dead?
Sure fire way to tell:
Go get one of those cigar end-cutters, put your finger in it, then chop it off. If blood squirts out of the end of your new finger stub, then the blood supply was ok and your finger wasn't dead. If it just dribbles out, then the blood supply was inadequate and your finger was probably going to die, anyway.
[LEGAL DISCLAIMER: THIS IS NOT MEDICAL ADVICE. IF YOU CHOP YOUR FINGER OFF, YOUR FINGER WILL BE CHOPPED OFF, AND THEN YOU'RE SH-T OUT OF LUCK, UNLESS YOU RUSH TO SURGERY AND HAVE YOUR FINGER RE-ATTACHED, WHICH WILL NOT BE VERY FUN AND COST A LOT OF MONEY.]