In the poem "Out, Out--," how does Robert Frost bring about the tragic death of the boy?

In his poem "Out, Out--" Robert Frost uses the juxtaposition of positive, warm details to emphasize the horror and unexpectedness of the boy's sudden death. The poem begins:

The buzz saw snarled and rattled in the yard

And made dust and dropped stove-length sticks of wood,

Sweet-scented stuff when the breeze drew across it.

The first line contains the negatively charged words "snarled" and "rattled." The associations to danger and bones create a frightening atmosphere. However, that atmosphere is quickly contrasted with the "sweet-scented" dust created by the saw. This creates a confusing tone - should the reader be frightened or not? That confusion heightens the suspense.

And the saw snarled and rattled, snarled and rattled,

The repetition here of the snarling and rattling begins to confirm the suspicion that the poem is going to have a bad ending.

Call it a day, I wish they might have said

To please the boy by giving him the half hour

That a boy counts so much when saved from work.

The inclusion of "I wish" foreshadows that something will happen to the boy that would have been prevented if they had given him "the half hour," or in other words, let him off early. This is immediately followed by another warm moment, as "His sister stood beside him in her apron / To tell them ‘Supper.’" This addition of a family member makes the incident that follows even more horrific, as the addition creates another layer of sympathy for the family who loses their son.

The boy subsequently accidentally cuts off his hand, and dies from the injury. This horrific moment is characterized by his plea to his sister:

‘Don’t let him cut my hand off—

The doctor, when he comes. Don’t let him, sister!’

This plea is darkened by the fact that his hand is already off. He perishes and then the doctors move on to other patients quickly, as quickly as the boy suddenly cut off his hand and lost his life.

Frost's juxtaposing of frightening details and warm moments creates a suspenseful atmosphere that is heightened by the ending where the doctors move on from the boy - dead and without a hand.

Hope this helps!