How does Robert Frost try to bring out the sadness of the boy's death in "Out, Out--"?

The title of the poem is a reference or an allusion to the play Macbeth. Upon learning of his wife's death, Macbeth talks about how fleeting and meaningless life is: 

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. (V.v.25-30) 

In...

The title of the poem is a reference or an allusion to the play Macbeth. Upon learning of his wife's death, Macbeth talks about how fleeting and meaningless life is: 

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. (V.v.25-30) 

In the poem, the boy dies too young. His life was much too "brief." The speaker in the poem wishes the boy had been given a break.

"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 boy is doing "a man's work." The speaker implies that, ideally, the boy should be playing or doing a boy's work. Unfortunately, the family needs the boy to work. So, his life is cut short and because he had to work, he has lost a significant portion of his childhood. 

There are more obvious attempts at empathy. The boy's cries not to have his hand cut off are powerful. The boy dies and the family returns "to their affairs." Here, the speaker is being very critical. The boy is dead and there is no mention of the grieving process. They simply go on with what they had been doing. The boy's shortened life is sad to begin with. The indifferent reactions of those around him make his life/death seem more sad and less meaningful. This is the connection to the quote from Macbeth. 

Is the boy's death simply a random part of nature? And if it is random, does that make it more senseless? Or is it a result of humanity's growing obsession with technology (the saw)? Frost does not answer these questions about death. He leaves it for the reader to decide. For some, this lack of closure adds to the meaninglessness and perhaps adds to the sadness of the poem.