Elizabeth Wolcott has noted that if Joker’s knives are his use of words, then we can account for Joker’s scars. Presumably the scars came from a knife; given that he describes his father cutting him up and him cutting his wife or himself up (I’m not sure of the latter, I forget what happened), and each actor in the story has something to say ending with “let’s put a smile on that face,” it’s pretty clear there’s a teaching at stake here.
We noted earlier that justice conducted via procedure is merely people making plans, people telling one another “it’ll be ok” no matter what awful thing happens because there’s a plan.
Words and knives are the exact same thing – you can kill with words, people who make plans do so every day. The Joker’s scars come from the words/knives. The difference between him and his victims is that he survived such an attack. He became ugly seeing ugliness.
The point might be that he thinks he’s doing the people he’s killing a favor by giving them a horrible, brutal experience before their death. He’s showing that some scars aren’t worth surviving, quite literally. Again, you can contrast with the battered, bruised Batman out of uniform we always see. You can also contrast their relation to money, too. Then you can see yet again why Joker’s point in the holding cell to Batman is accurate – all will turn on you too when they feel you have no use.