What does the line " I cut the pig's throat, said Jack, proudly, and yet he twitched as he said it" show about his murderous capabilites in Lord of the Flies?
The quote that you are referring to comes in chapter 4. It is Jack's first successful pig hunt and his first kill. The simple answer to your question is that the quote shows that Jack is capable of killing. The twitch could indicate one of two things. One, he feels a bit grossed out by the kill and gets one of those "fully body shivers." Two, he feels powerful and invigorated from the kill and the twitch indicates his body's excitement to do it again. I would go with the later, since killing gets easier and easier for Jack as the novel progresses. Not only easier, but Jack graduates to killing humans, too.
The quote comes after Ralph expresses disappointment and anger at Jack for letting the fire go out. Jack's response isn't an apology. Jack's response indicates that he believes his personal desires (in this case hunting) take precedence over orders received and over the good of the group. Jack is more or less telling Ralph that the fire doesn't matter because he killed a pig. The quote shows that Jack highly values the thrill he gets from killing.