Its not exactly a common expression. I've never heard of it before, and I doubt anyone would say it in real life. I've never heard the song, but I would guess that the speaker is trying to quit drinking alcohol, and that the other person is stressing them out so much that it's driving them to drink.
That the word "twist" is used implies that any damage to their sobriety is temporary, so basically, it's a fancy, poetic way of saying both "you're driving me to drink" and "you aren't important in the long run".
Again, I've never heard that expression before, but that's how I would interpret it.