The blokova lost her third finger because of the escape attempt led by Shmuel and Yitzchak. Even though the attempt was a failure, the fact that it occurred at all showed that, in the twisted hierarchy of camp organization, she had lost control of the prisoners under her watch.
The blokova is a Jewess who is put in charge of other Jews in the camp by the Germans. Her responsibility is to keep the Jews in line, and "if she loses control of her zugangi", the inmates in her care, she is punished by having a finger chopped off. The blokova had lost her first finger awhile back, when a group of zugangi rioted, and her second finger sometime later, when six zugangi hanged themselves one night. These incidents, like the escape attempt, were interpreted as a lack of leadership on her part by the Germans, and the consequence of such lapses in responsibility is the barbaric practice of removing one of her fingers for every lapse (Chapter 16-17).