In thinking of Boxer as a tragic hero, I think that a couple of elements have to be present. On one hand, I think that Boxer is unaware of his own predicament. This helps to make him quite a tragic victim of his circumstances and surroundings. Boxer is manipulated by Napoleon in order to maximize his effort and when he is deemed ineffective, he becomes a victim of his circumstances. I think that Boxer can be seen as tragic in that he is made to realize, albeit too late, that he is being taken to the Knacker's. Clover screams this out to him as he is being taken away, and as he kicks the sides of the truck that has come to take him, his resistance is futile. In the end, this becomes a tragic end to one of the most heroic and noble characters in the novel.
With all of this in mind, I am not entirely certain that Orwell was really concerned with establishing Boxer as a tragic hero. In some senses, Orwell feels much in way of sadness for Boxer and his representation of those who blindly serve their political rulers. Yet, there is a level of anger that Orwell possesses for Boxer, precluding him from being fully embraced as a tragic hero. In the end, Orwell feels that Boxer's willingness to blindly follow Napoleon, confirmed with his assertions that "Napoleon is always right" and "I will work harder," coupled with his lack of learning the alphabet in not being able to get past the first four letters, and his lack of questioning all play a role in Boxer's downfall. This might not make him tragic as much as simply making poor choices in relation to himself and authority.
He is the farm's most hard-working and loyal laborer. Boxer serves as an allegory for the Russian working-class who helped to oust the Czar Nicholas and establish the Soviet Union, but were eventually betrayed by the Stalinists. The most sympathetically drawn character in the novel, Boxer epitomizes all of the best qualities of the exploited working classes: dedication, loyalty, and a huge capacity for labor. Exploited by the pigs as much or more than he had been by Mr. Jones, Boxer represents all of the invisible labor that undergirds the political drama being carried out by the elites. Boxer’s pitiful death at a glue factory dramatically illustrates the extent of the pigs’ betrayal. It may also, however, speak to the specific significance of Boxer himself: before being carted off, he serves as the force that holds Animal Farm together.