Your intriguing situation is covered by literary license as noted in the last line of @lbf's answer. According to Wikipedia,
Artistic license (also known as art license, historical license, dramatic license, poetic license, narrative license, licentia poetica, creative license, or simply license) is a colloquial term, sometimes a euphemism, used to denote the distortion of fact, alteration of the conventions of grammar or language, or rewording of pre-existing text made by an artist in the name of art.
The operative concept here is
alteration of the conventions of grammar or language
and the meaning is established by context. But the way you found it written,
she pulled back her fingers a second before they were sliced off
makes the meaning extremely clear and unequivocal to habitual readers of English (that her fingers just escaped being sliced off) although the most unambiguous and "correct" way of writing it would be
She pulled back her fingers a second before they could be sliced off
where "before + could" clearly establishes that the event did not occur, as rightly pointed out in the earlier excellent answer of @Tuffy.
But authors don't care.
Moreover, this type of usage with "before" being used to describe just avoiding something happening is a well established convention of its own in both the spoken and the written language, as the other answers already attest; random examples:
The rope pulled him up just inches before his head hit the ground (as in bungee jumping)
They managed to save their marriage before it collapsed
Get in out of the rain before you catch a cold.