“Kill the pig, cut her throat….". I think this is more than a sentence. Can you explain me the deeper meaning of this quote?

The main point of this quote, which is a chant uttered by the boys as they participate in a somewhat frenzied and primitive dance around the fire after eating pig killed by Jack, is that it is savage in nature.  It shows how the boys are devolving; they are becoming less civilized, returning to a time of savagery. When Jack killed the pig, he cut its throat.  This method of killing is up close and personal, thus even more brutal.  The boys are championing this brutality in the chant. One of the reasons Golding wrote the book was because he was appalled at what mankind could do to one another after having seen what happens in war. He wants the reader to get the feeling of savage nature and the boys' chant and dance around the fire displays that. The rest of the chant is "Spill  her blood."  This is what people do to one another in war - spill blood.  Golding believed that everyone has an inner beast only kept in check by one's desire to keep it in check and by society's rules.  He uses this chant to show that the boys are letting out their inner beasts, some more quickly than others, but all are beginning to participate in this unleashing.