The title of the poem is famous, partially because the title of the super-bestselling book in which it was first published is 20 Love Poems and a Song of Despair. It's like the love poems are opening for the headliner, "A Song of Despair."
The poem has a lot of songlike qualities like repetition and, in the original Spanish version, almost all of the lines have 14 syllables, giving it a nice rhythm. The Spanish version also has assonant rhyme in every single even line, so the title of "song" makes more and more sense all the time. See "Form and Meter" for more on this.
It's interesting that the collection of love poems, which are really mushy, ends with this sad, hopeless song. That gives you an idea of the overall message of the poet, who ends not only this poem, but also his entire collection with the line, "It is the hour of departure. Oh abandoned one." Despair indeed.
Should we think of this as undoing the work of all the love poems that come before the "A Song of Despair"? Probably not. In fact, this poem is just as romantic and lovelorn as the best of the love poems. The collection really does all fit together in tone and message, but the "Song" comes at the end almost as a coda, or an epilogue, that reinforces just how strong the feelings are in the love poems.