Lyric discussion by the_boatman 

Cover art for Sorrow's Child lyrics by Nick Cave and the Bad Seeds

This song is full of symbols and metaphors, and should not be taken literally, so I don't think it's about a girl killing herself, as mentioned above. I think it's about trying to fight a mental state and emotion that makes the person feel as if they are being dragged under. I stumbled upon the following quote by accident, but it made me see the song in a new light, since Nick mentioned that he used to take heroin to stop all the thoughts and voices/songs/stories in his head and just be 'normal':

"Genius is sorrow's child."
Adams, John