Every time fingerprint scanners are mentioned, people start talking about cutting off fingers. Guess what: the people making the scanners have considered this scenario. All of their clients have nagged them about it continously for decades. It's fun to talk about, but it won't work.

It'll work fine if the scanner isn't fancy enough to include "live finger" detection tech like matching the veins beneath the skin's surface (https://en.wikipedia.org/wiki/Finger_Vein_recognition).