The scene in which Bill the Butcher uses the empty carcass of pig to demonstrate how to kill a human is very interesting. It immediately follows the scene in which Amsterdam sees another of the men who were once with the Dead Rabbits when he was a child.
The lighting is pretty normal, with daylight shining on the two of them inside the dark Butchers. Something about the light and the music creates a sort of intimacy between the two men, despite the morbidity of their actions. Bill becomes almost this sort of fatherly figure, instructing the young Amsterdam, who initially is curious and trusting.
The music from the previous scene flows into the music of the Butcher scene, and it is a bittersweet, lilting string solo. This music is maintained throughout this scene, even as the two of them hack at the flesh of the pig. The music actually gets louder when Bill passes the knife along to Amsterdam, increasing the intensity of the scene. As Amsterdam hacks at the pig, a more ominous sounding music layers over it to transition this scene to the next.
When Bill hands him the knife, the camera flashes to posters commemorating the Victory of the Natives over the Dead Rabbits, and then to a flashback of Vallem handing Amsterdam the razor 16 years before. This shows that Amsterdam has not forgotten how Bill took his father’s life. He shows some indecision, but quickly and precisely imitates Bill in stabbing the pig. The viewer is left wondering why this scene is important. Is Amsterdam joining in Bill’s efforts? Does he have any wish to continue in his father’s footstep in defending his Irish brothers and sisters? All we see is his indecision, but violent ability.