Lyric discussion by akanakin 

The first three paragraphs of this song detail Mayo's interrogation of Sizer. He is an IRO-bot, a robot, so instead of just killing him, Mayo literally chops his limbs off with a chain saw - "sever the limbs from his torso."

The next part starting with "slowly discarded" detail how Mayo tosses Sizer's remains in an alleyway. Claudio, Coheed and Cambria's son, who has been a recluse the past decade, stumbles upon his remains while arguing with Ambellina. He recognizes it as an IRO-bot, something Claudio is as well. He "fixes and restores" him.

The last part, "pull the trigger and the nightmare stops," harkens back to the interrogation. It is something Sizer was yelling at Mayo, begging him to kill him so that the interrogation can end.

Your interpretation to the last part is pretty close but Sizer wasn't really "begging" per say for Mayo to stop. It was more like "Pffft, I wish you would". By that point he didn't really have anything left to loose and death would be nothing but a relief.

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