I suggest beginning with the origins of the title as Macbeth's lament after the suicide of his wife Lady Macbeth (from the play by Shakespeare). There is with both deaths an inconvenience suggested. Macbeth is in the midst of fighting to retain the crown, and the woodsman have a job to finish. Both deaths seem to be more of a momentary diversion than a greatly mourned loss.
The poem makes great use of sibilance (repetition of the 's' sound) to emphasise the menacing action of the saw, and the boy's life ebbing away.
The buzz saw snarled and rattled
Frost also makes use of the caesura (an unnatural pause within a line) to suggest the interruption and halting of the day's work - and the life of the boy.
So. But the hand was gone already
The saw is also personified to suggest it is as responsible for the accident as the boy's carelessness or his distractor's voice. It gives the saw a cruel appearance too.