I would say the manner in which Napoleon addresses potentially problematic situations is fairly ruthless. His elimination of Snowball would be one such example. Yet, even if one could chalk this up to political pragmatism, his elimination of Boxer is really ruthless and quite heartless. After extracting all he could from Boxer in terms of his work ethic, taking what he could regarding the building of the windmill, and after Boxer had given the best he could, Napoleon arranges for him to be shipped off to the horse slaughterer. It is really harsh and ruthless because once Boxer is unable to give anything else to Napoleon, he is deemed unimportant and arrangements are made to "get rid" of him. In this, one sees Napoleon's cruel and heartless nature present.
He is ruthless in a way that he eliminates any opposition, any dissidents to his rule which might bring him harm as he consolidates his power. He is a ruthless dictator and he only cares about his own power and comfort. To achieve all this, he resulted by mass murder, starvation and also the re-writing of history to turn Snowball, who was a hero into a public villain, despised by many. He degenerated into a senseless monster by killing Boxer, who was injured by then, for profit by sending him to a slaughter factory in exchange of a few bottles of whiskey. From this, we can see he is a heartless beast who does not care about anybody, only if it suited his own interest. His rule of terror brought widespread suffering and fear amongst the animals in the farm.