How does the poet convey sadness about the boy's death in "Out, Out—"?

Robert Frost's poem "Out, Out--" is a simple and sad story of a young boy who cuts off his hand in a work accident and ultimately bleeds to death. The poem is not only a comment on the brevity of life but also its meaninglessness, as evidenced by the title of the poem which is an allusion to Macbeth's speech about the death of his wife:

Out, out, brief candle!
Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.

Little, less, nothing!--and that ended it.
No more to build on there. And they, since they
Were not the ones dead, turned to their affairs.

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.

Then the boy saw all--
Since he was old enough to know, big boy
Doing a man's work, though a child at heart--
He saw all spoiled.

How does the poet convey the sadness of the boy's death in "Out, Out—?"

The poem recounts a day when the men and boys are working in the yard cutting firewood with a buzz saw. The setting is in Vermont, where five mountain ranges can be seen in the background. It is just about dusk, and the men have been working all day. The boy is operating the buzz saw, cutting larger logs into "stove-length sticks of wood," when his sister comes to announce that supper is ready. At this the boy becomes distracted, and the whirling blade of the saw meets the flesh of his wrist, severing it nearly completely. The doctor arrives and administers an anesthetic, but as he is doing so, the boy dies, presumably from shock and loss of blood.

The poet conveys sadness by the narrator, known only as "I" in the poem, saying, "Call it a day, I wish they might have said." If the work had been called off an hour sooner, giving the boy a half hour to go and play, the accident would never have occurred. The exclamation, "But the hand!" and the description of the boy's "rueful laugh" brings a horrifying sadness. The poet puts the reader in the boy's mind, saying that as he held up his dangling hand, he "saw all— / Since he was old enough to know, big boy / Doing a man’s work, though a child at heart." The reader feels sadness knowing the boy had been working so hard, yet he really was just a child. One can't help thinking at the same time that the parents and all the adults there would be blaming themselves for allowing so young and inexperienced a person to run such dangerous equipment.

When the boy pleads with his sister to not let the doctor cut his hand off, it is almost unbearable to imagine the scene. The pronouncement that "the hand was gone already" is somber, but then comes the stunning description of the boy's life slipping away before the reader's eyes: "Little—less—nothing!—and that ended it." With agonizing understatement, the poet sums up the finality of death: "No more to build on there." Though the last line seems cruel, describing how those who were not the one who was dead "turned to their affairs," it is a numbing commentary on the fact that life goes on for the living even after unspeakable tragedy.