Lyric discussion by timothyjonking 

His baby is Heroin, which he is comparing to a lost love. In many cities the junkies would hang out by the river and shoot up. "SHOT HER DEAD" means he used up all of the Heroin, and to a junkie it's like killing a love. Neil Young has a few songs that are about drugs (The Needle and The Damage is Done and Sugar Moutain, so why would it be so strange that this is about drugs?

"she could drag me over the rainbow, send me away Down by the river I shot my baby Down by the river, Dead, oh, shot her dead."

I think the same. Doesn't have to be about H, but I think this too.

He rails against heroin in The Needle and the Damage Done although that doesn't prove he didn't try it.

Also and admittedly a bit literal 'shot my baby' could mean ejaculate, have sex.

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