Napoleon, like many brutal dictators, executes animals to keep his subjects under his control. If the other animals see that they face the risk of death if they rebel or even question Napoleon's rulings...they will most likely not break the rules. Creating fear is a common tactic for rulers who don't want individuals to break from the common goal.
Napoleon bans the singing of "Beasts of England" because that was the song of the last rebellion. It was a song that reminded the common people that they wanted a world where they had a voice and all of them were equal. Now that Napoleon has turned Animal Farm into the same (or worse) kind of farm that Farmer Jones had...he is afraid that the rebellion song will stir up the people to rebel against him.