I've tried looking up phrases like cut off finger bleed to death, lose finger bleed to death, what happens if I lose a finger -nail, bled to death from finger, how much blood from cut off finger, etc. Most of the results seem to be from Yahoo Answers and similar sites, with answers that range from "OMG yes" to "of course you won't". The rest were anecdotal or irrelevant. (I'll admit I might have been able to do better, but I can only handle so many graphic descriptions of gore and blood loss.)
Most of what I've heard in real life would seem to suggest that it won't immediately kill you, but obviously people in this day and age do tend to themselves somehow and don't immediately rush into a long swordfight, which is what I want to know about. Can a person bleed to death from a lost finger? How quickly might it take effect, from weakening them noticeably to actually killing them? Even if it wasn't lethal, how much blood could they expect to lose?