The joke here is that Joker, who is particularly fond of jokes, is tearing up a newspaper in rage at being explained a joke. You see, he believes that humor is best expressed through what's not said, and that brevity is the soul of wit. The humor of this joke is derived from the fact that, in joker explaining what makes a joke unfunny, he himself is making a joke, by explaining to the audience what made the joke unfunny. This type of humor would be exactly to the Joker's liking, and is thus in-character for him, as he's not explaining this joke, but is rather frustrated at the explanation of another. The framing of Harley Quinn seemingly being thrown to the ground by the enraged Joker further contributes to the humor found within this joke.