The poem describes a boy who is sawing wood. This boy initially seems distracted, and he lifts his eyes from the saw to look at the "five mountain ranges" in the distance. The boy escapes this first lapse of concentration unscathed, but he does not escape the next. When his sister calls him in to supper, the boy loses his concentration once more and the saw leaps out of his hand.
Immediately after the saw has cut through the boy's hand, he turns "toward them holding up the hand." The "them" mentioned here and elsewhere in the poem are likely the boy's workmates. At the end of the poem, the boy dies, and these people, referred to as "them," seem unmoved and indifferent to the boy's death. Indeed, Frost writes that "they, since they / Were not the one dead, turned to their affairs." From this reaction it seems safe to assume that these people referred to as "them" are not the boy's family or friends. They seem to have no emotional connection to the boy.
After the boy, the next most important person in the poem is the boy's sister. It is to his sister that the boy appeals after the saw has cut through his hand. He begs his sister to not let the doctor cut his hand off, exclaiming, "Don't let him, sister!"
When the doctor arrives, he is unable to do anything to help the boy. The doctor "puts him in the dark of ether," but the boy dies shortly after. Perhaps the implication is that the doctor is ultimately responsible for the boy's death.