How does this poem sound when you read it aloud? Go ahead, we'll wait.
OK, now that you've read the entire poem aloud to yourself (or at least the first few lines), notice how good Frost is at melding flow with stop. So, when we're reading about sunsets, scenery, or things like that, the poem goes pretty smoothly without cluttered punctuation. But when Frost wants us to stop, with a "So" or a "no one believed," it halts dead in its tracks.
Take line 25 as an example: "He saw all was spoiled. 'Don't let him cut my hand off—.'" In the first sentence, we begin with a smooth flow (including the grim "saw" pun) until we hit the word "spoiled." The verse then immediately jumps into the boy's voice, which echoes in your head creepily.
Also, note how effective Frost's use of alliteration is: "day was all but done" (9). The dull throb of those D words implies a certain finality to things. All the H alliteration in "He must have given the hand. However it was," creates a kind of breathless rush that adds to the urgency surrounding the accident. The sounds of the poem, then, reinforce the poem's content, drawing our ear toward its focus.