In his editorial on Tom Robinson's death, Mr. Underwood "likened Tom's death to the senseless slaughter of songbirds by hunters and children." The point that Mr. Underwood is making here is that Tom was a victim of the senselessness of man's judgment. A songbird (or "mockingbird" as the book's title references) is a creature that does no harm to others, but rather offers something sweet, simple, and lovely to the word: its voice. However, because the world is cruel and quick to stomp out all that is good, these animals often face damage and death; in much the same way, Tom was at the whim of those with far greater power and privilege, and he suffered greatly as a result of it. Although he was physically incapable of committing the crime he was accused of due to his crippled arm, Tom was found guilty and sent to prison. This action was like targeting a sitting bird.
Scout realizes that although Atticus was able to defend Tom in a court of law, giving the accused man his due process, Tom was "a dead man" as soon as Mayella Ewell made the accusation against him. As she articulately mentions, Tom had no true case in "the secret courts of men's hearts."
Mr. Underwood does not explicitly use the word "mockingbird" but he does say that Tom's death is like what happens when hunters and kids kill "songbirds" for no reason at all.
What Underwood is saying is that the people with power are hurting those who have no power (like a person shooting a bird). Moreover, he is saying that those with power are doing this for no good reason -- just because they can -- just as there is no good reason to shoot a songbird because you can't eat it.
So Underwood is arguing that some whites are simply abusing their power because they can.