It ain't called "A Song of Despair" for nothin'! This poem really wails. It's a sad song, a breakup song, a lament. This guy has got the blues and he is letting it out musically.
Of course, when you talk about the sound of this poem, it's crucial to realize that there are two sets of sounds to think about: the sound of the Spanish original, and the sound of the English translation. In both cases, though, both Neruda and his English translator, W.S. Merwin, give our ears a lot to chew on (if you can imagine that image).
For example, there is a lot of repetition here that might remind you of a song's chorus, like "Oh pit of debris" or "In you everything sank!" The way those phrases keep coming back—in English or Spanish—marks them as refrains, or key ideas that this poem is trying to underscore for the reader or listener.
Then there's the alliteration. Many of the lines repeat the S sound, which reminds us of the sound of waves sizzling over the sand:
The river mingles its stubborn lament with the sea. (2)
Now, this doesn't translate exactly from the Spanish, but there is alliteration in the original Spanish version, too. Check it out. The same line quoted above in Spanish is:
El río anuda al mar su lamento obstinado.
While we may not have as much S-alliteration in the Spanish version, we still have sound to consider here. In this case, you get much more assonance with the repeating A (ah) sound, which might make us think of someone crying, or sighing.
In short, whether it's the Spanish original, or Merwin's pretty faithful translation, this poem uses sound to remind us that it's a song, meant to be heard aloud. As well, those sounds that find its listeners' ears subtly reinforce its key ideas, however sad and lonely they may be.