A "tragic hero" of course is quite different than someone who has "tragically heroic traits." A tragic hero brings about his own ruin through some fatally harmful character trait or erroneous decision. "Tragically heroic traits" define a person who performs an heroic deed only to meet with horrifically painful end results. Haemon was heroic because his honor and noble mien enabled him to stand up to his father and against his father's wrong deeds. He was tragically heroic because the course of justice and right led him to take his own life rather than comprise justice and mercy by tacitly siding with his mistaken father.
The earlier posts are very strong. In his Poetics, Aristotle argues that the most powerful tragic situations often involve members of the same family, especially when a person is torn between two powerful allegiances, as Haemon is torn between duty to his father and love of his fiance.
Interestingly, Aristotle's only explicit reference to Haemon occurs when he is discussing the four different ways in which what he calls a "deed of horror" may be staged. He concludes his discussion by saying,
of all these ways, to be about to act knowing the persons, and then not to act, is the worst. It is shocking without being tragic, for no disaster follows. It is, therefore, never, or very rarely, found in poetry. One instance, however, is in the Antigone, where Haemon threatens to kill Creon. (S. H. Butcher translation)
I agree with other editors. This is a play in which Haemon displays a love of Antigone that is so strong that it overpowers everything else, including his sense of loyalty towards his father and the state and, ultimately, life itself. This is why his love for Antigone, in spite of its purity and goodness, can also be viewed as Haemon's tragic flaw. He literally finds life unliveable without his love and so decides to join her.
There are two elements that are necessary for a figure to be tragic. First, he or she must be noble. In the case of Haemon this works, because he is the son of Creon, the ruler of Thebes. Second, the tragic figure has to have a good quality that leads to his or her demise. In the case of Haemon it is his love and loyalty to Antigone. What makes things a little more complicated is that Haemon is made to choose between his father and his lover. In the end, he commits suicide with Antigone.
I think that one of Haemon's most tragically heroic traits is that he is loyal. He is extremely loyal to Antigone. He cannot conceive of life without her and when he finds her dead, he can no longer bear to live. I would say that this is one of his tragically heroic traits for loyalty is heroic, but it ends being the root of his tragic end for he dies as a result. I would think that another trait that ends up operating in a tragic sensibility would be his sense of love. Of all that is present in the drama, Haemon's love for Antigone is probably the most pure. He simply loves her to the point where he is willing to repudiate the bonds with his father as a result of it. Haemon's love of Antigone is tragic because it ends up spelling the doom of the family, resulting in his death, the death of his mother, and Creon's revelation that he pursued the wrong path in this particular situation. In Haemon's love, there is an absolute sense of devotion and emotion that is transcendent of all temporal and contingent conditions that surround him. In this, there is heroism, but results in tragedy.