The acts of murder that occur in the story are a way of showing the breakdown of social order. The boys, away from the strict rules and structures of their school, are shown to be capable of violence, cruelty, and tyranny. Because Jack's "tribe" rebels against Simon and Piggy, the de facto "leaders" due to their intelligence and desire to maintain order, it can be seen as a rebellion against the same sort of social order and leadership they had back home before their exile on the island. "Pig" is a slang term for law enforcement and it is possible that the slaughter of Piggy is symbolic in this way: a killing and destruction of social order, authority and rules of law (such as the use of the conch for speaking).
The pigs of the island are also a sort of authority presence, since they have lived there for a long time and know the environment; they have a sort of expertise and wisdom regarding this place that the boys do not. The pigs are like an elder indigenous tribe of the island, knowledgable of its traditions, and in that way deserving of respect. By killing the pigs recklessly, especially the mother pig who could have helped provide a more sustainable food source, the boys are literally murdering wisdom and tradition. Piggy's murder is similar: by killing him for wanting to exercise a traditional sort of leadership and logic, Jack and his followers are overthrowing the old rules in favor of a sort of anarchy based in selfish needs instead of logic, order and cooperation.