Biographically, it seems that Robert Frost had an event like this occur in his life—his neighbor was a young man who sliced his hand on a saw and later died. Remember, though, readers, Frost is not necessarily the speaker in the poem. Instead, he wrote the poem from the perspective of the speaker.
And that speaker here is a third-person observer who seems to be sorting through what happened—he dwells on events that took place over the course of milliseconds, and seems to try to understand what role the saw played in the event. He depicts the transition from concern to callousness that occurs when the boy dies and is no longer fit for work, but does not comment on it. There's no line here that says, "And the family disregarded the boy, and they're bad for doing it."
Think about what it means that the speaker is detached. This is a tragic scene, and yet the tragedy of it seems totally lost on the boy's family. They turn to "their affairs" rather than the boy's arrangements or, you know, anything like grief. For the speaker, this means that his voice echoes that of the participants. There is an emotional disconnect here that allows us to approach this tragedy from the perspective of work. There is "no more to build on" in this vicious cycle of work to avoid death, and death caused by that same work.
The cycle is all the more tragic because the reader is forced to fill the void the speaker has left in terms of empathy. The speaker presents this story without over-the-top emotional commentary, but that reserved silence allows us, as readers, to interject our own sense of loss and outrage at the boy's senseless death. By playing it cool, the speaker allows us to be the ones getting heated up about this tale.