Act III.1 starts with Titus shedding a semiotic rainbow of tears. His first tears are pleas, like Tamora's tears in Act I, and equally ineffective. They should evoke pity for his sons in the addressees, the senators:
And for these bitter tears which now you see
Filling the aged wrinkles in my cheeks;
Be pitiful to my condemned sons"
His next tears become ink, and the earth a blotting paper:
For these, Tribunes, in the dust I write
My heart's deep languor and my soul's sad tears.
Let my tears staunch the earth's dry appetite;
My sons's sweet blood will make it shame and blush."
And finally the personified tears should "speak" themselves as multiplied clones of their sender, the crying father: "My tears are now prevailing orators"
Lavinia and Marcus then join him in a choir of tears with a crescendo. "When I did name her brothers, then fresh tears / Stood on her cheeks" Lavinia's tear language is immediately interpreted, although the meaning of her message is again ambivalent:
Perchance she weeps because they killed her husband,
Perchance because she knows them innocent"
The first scene is also dramatic because of Aaron's aside, in which he says, while tricking Titus into cutting off his own hand, "O how this villainy / Doth fat me with the very thoughts of it! / Let fools do good, and fair men call for grace; / Aaron will have his soul black like his face" This statement can be taken in two contrasting ways. It can be seen as locating Aaron's evil within his blackness, as popularly accepted in racial stereotypes. Alternatively, it can be taken as proof that his villainy is a deliberate choice rather than the natural characteristic of a Moore. Either his soul is inherently black because he is black, or he decides to make his soul black because he has been treated so badly for simply having black skin.
The second scene is one of the most dramatic. In it, Titus enacts his first role as cook/feeder, in this case to his daughter Lavinia (later he will feed a horrendous feast to Tamora). This marks the only time in Titus when eating is portrayed as a natural and even nurturing act, as opposed to the ravenous, corrupt appetites portrayed in other parts of the play. In this scene, the textualization of Lavinia's body begun by Marcus in Act II Scene IV is completed as she is described as a "map of woe" whose sign language must be interpreted. From her mute motions, Titus says that he will "wrest an alphabet" The role of Lavinia is very important to consider as a symbol of theatricality in the play. She becomes central to the play (as a reason for revenge) just when she loses her ability to speak and is left with no communicational means but her gestures. This draws our attention to the fact that this is a play to be staged, and that Lavinia is to be looked at and not just heard.
Most of the characteristics we associate with tragedy come from Aristotle's Poetics, which was his analysis of the most famous Greek playwrights. Shakespeare did not follow many of Aristotle's principles, which is why he would have written a tragedy like Titus Andronicus, one thing common to all tragedy is that there is no formulaic happy ending. It does not matter who is alive or dead, they are not happy about what has transpired. This is in contrast to comedy which usually ends in a wedding. Aristotle also calls for the audience to experience a catharsis, as does Shakespeare.
I would say that it boils down to who has more authority: Aristotle or the playwright writing the tragedy. Shakespeare does not follow many of Aristotle's dictums, but he definitely has the authority to flout them and still be taken seriously.
Aristotle sets forth many criteria for tragedy. The most prevalent were the unities of time, place, and action. Shakespeare flouts this criteria, I would say, especially in Titus.
Hamartia is also often erroneously described as a fatal flaw." It is more correct to describe it as an excessive quality (good or bad) that is inappropriate or out of context with the situation at hand. Titus is a good example of this. He is set in a situation which calls for him to exact revenge, yet unlike the protagonists of typical revenge tragedies of the time he is too humane and principled to rush out and do it. but rather is taken on a whirlwind of emotion before finally doing it. The play is not about revenge, but about his coming to grips with what the situation requires of him.