How does the writer bring out the sadness of the boy's death by the reaction of the people?

There is actually not a lot of sadness that is expressed for the boy's passing in this poem. The first emotional reaction to the incident comes from the boy, himself, when he gives a "rueful laugh" (19) at the saw cutting his hand––rueful, because he is part surprised and part shocked but is not feeling the pain yet. Then, when "the boy saw all–– / Since he was old enough to know... He saw all spoiled" (22-25). The boy understands that this incident is serious, and he begs his sister not to allow the doctor to cut off his hand.
The second emotional reaction comes from the doctor, described as "the watcher at his pulse" who takes "fright" (30). But "[n]o one believed" that the boy would die from this incident (31). They all stand by and listen as the boy's heart stops beating; the only reaction indicated by the author is the use of the exclamation point as the heart stops: "Little--less--nothing!" (32).
The end of the poem shows the least emotion from everyone, including the author:

... and that ended it.
No more to build on there. And they, since they
Were not the one dead, turned to their affairs.

The short, declarative sentences simply state that everyone went back to their work and their lives. There does not seem to be any sort of reaction from the family, though the reader knows that there is, at least, the boy's sister there with him.