Mr. Underwood’s quote demonstrates that Tom Robinson is a mockingbird because he is crippled and targeted by society for no reason.
When Atticus gives his children Beebe guns, he tells them shoot “all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird" (ch 10). The children ask Miss Maudie what that means, and she explains that mockingbirds don’t hurt anyone so you shouldn’t hurt them.
There is a direct connection between this quote and Mr. Underwood’s reaction to Tom Robinson’s death. He is shot trying to escape from prison, and they said he would have made it if he had not been injured.
Mr. Underwood simply figured it was a sin to kill cripples, be they standing, sitting, or escaping. He likened Tom's death to the senseless slaughter of songbirds by hunters and children…(ch 25)
Of course, it is almost as if he heard what Atticus said. Mr. Underwood appreciates that Tom Robinson should not have been killed. Besides being targeted for his race, Mr. Underwood feels he was targeted for being a cripple. He considers this unfair.
When Mr. Underwood compares Tom’s murder to a child killing a songbird, he is scolding the town on its attitude toward senseless violence. Unfortunately, the townspeople just think he is trying to be eloquent to get his editorial reprinted in a larger paper, and they do not take what he says to heart.