They are both driven by vengeance. Tamora hates Titus Andronicius for killing her youngest son as the sacrifice and starts her schem of revengeance. While Titus Andronicius shoulders all the humiliation and suffering of seeing his sons die one after the other, and finally finishes his task.
The meat pie is filled with the ground up bodies of Tamora's two sons Chiron and Demetrius.
Tamora the Goth Queen and Empress of Rome, disguised as Revenge, has proposed to Titus that he should invite the Emperor and Tamora to a dinner party along with his son Lucius who is leading an army of Goths toward Rome. At this party, Tamora-Revenge says, he can get revenge on his enemies. Titus has been driven half-crazy by the deaths of two of his sons and the rape and dismemberment of his daughter Lavinia by Tamora's sons, and so Tamora believes that he does not have a good enough grip on reality to be able to actually take revenge on her and her sons. But she is wrong. Titus lures the sons into a trap and kills them. At the dinner party, Titus is the congenial host, and serves Tamora a delicious meat pie. When the Emperor calls for Tamora's sons, Titus delivers the punchline: "Why, there they are both, baked in that pie whereof their mother daintily hath fed, eating the flesh that she herself hath bred." While she's gagging, he knifes her. But the Emperor immediately thereafter kills Titus and Lucius immediately kills the Emperor, so that within seconds the table is covered with corpses.
Shakespeare's plays are intended to entertain, not to instruct, but Shakespeare's early revenge tragedy Titus Andronicus provides an example of hatred and revenge spinning out of control. Tamora's hatred of Titus, and subsequently Titus's hatred of Tamora spills out so that it taints everyone and everything associated with the hated one. Tamora's revenge against Titus for the death of her son encompasses two of his sons, his daughter and his son-in-law. Titus's hate for her encompasses Aaron, Chiron and Demetrius as well. The extent to which this happens is shown in Act III Scene ii when Titus upbraids Marcus for killing a fly, and Marcus responds "it was a black ill-favour'd fly, like to the empress' Moor; therefore I kill'd him.", and Titus attacks the fly, saying "there's for thyself, and that's for Tamora". Even the fly gets attacked because it looks like Tamora's lover, because that somehow attacks Tamora as well.
Assuming the Andronicus you are referring to is Titus Andronicus, the main character in the Shakespeare play, his death is only semi-public. A private dinner is arranged to reconcile the Romans and the invading Goths including the Emperor, the Empress and Titus's son Lucius. It's a private function but it is also a state function, so it is well-attended. Titus uses the opportunity to get his revenge on his enemy Tamora, but he is immediately killed thereafter by Tamora's husband Saturninus.
Titus Andronicus. In order to torment her enemy Titus, the Empress Tamora dresses up as the embodiment of revenge while her sons Chiron and Demetrius portray murder and rapine. Their belief is that Titus has by this time lost his mind and will be unable to recognize them. Unfortunately for them, they are wrong.
Shakespeare only describes the characters in his plays through the mouths of other characters, so it is never Shakespeare speaking. Lavinia describes her as "barbarous Tamora", and Tamora claims she and Bassanius called her "foul adultress, lascivious Goth". Saturninus calls her "Lovely Tamora, Queen of the Goths, that like the stately Phebe 'mongst her nymphs dost overshine the gallan'st dames of Rome". Obviously neither of these is Shakespeare speaking.
The most famously gory of Shakespeare's plays is Titus Andronicus, which not only features a large number of murders of various kinds, but also a rape, after which the rapists cut off the rape victim's hands and cut out her tongue so she cannot identify them. The main character is persuaded to cut off his own hand in an effort to save the lives of two of his sons who are executed anyway. Two people are cooked and fed to their mother for supper. The play ends with Titus killing his daughter Lavinia (the aforesaid rape victim), his enemy Tamora and her husband, while he himself is killed. His last remaining son and brother execute Tamora's lover by burying him alive. Actually as many people die in Hamlet as do in Titus, but Titus wins the blue ribbon for sheer grisliness.
Titus Andronicus. He feeds this human pie to his enemy Tamora and her husband Emperor Saturninus, who are both responsible for the deaths of 2 of his sons and the rape and dismemberment of his only daughter.
It's much easier to say who doesn't die: Marcus Andronicus, Lucius Andronicus and Young Lucius. The ones who do die are Titus and his children Mutius, Quintus, Martius and Lavinia, Tamora and her sons Chiron, Alarbus and Demetrius, Saturninus and his Brother Bassanius, Aaron (although he actually dies after the play is over, since it ends with him being sentenced to death) and a Nursemaid. Thirteen in all. We're not counting Titus's dead sons that are buried in the first scene of the play.
Philemon is in the NT after Titus and before Hebrews.
The cast of Titus Andronicus - 1985 includes: Eileen Atkins as Queen Tamora Michael Crompton as Chiron Deddie Davies as Nurse Paul Davies Prowles as Young Lucius Nicholas Gecks as Bassianus Edward Hardwicke as Marcus Tom Hunsinger as Martius Neil McCaul as Demetrius Michael Packer as Mutius Trevor Peacock as Titus Andronicus Brian Protheroe as Saturninus Hugh Quarshie as Aaron Crispin Redman as Quintus Gavin Richards as Lucius
Well, I am not William Shakespeare, but since he's dead I hope you don't mind if I answer. The multiple deaths in Act Five are the inevitable result of responding to injury with injury. Except killing Lavinia--that was just gratuitous. The whole play is about escalating revenge: Tamora taking revenge for the death of Alarbus, then Titus takes revenge for that revenge and so on. By Act five it is a frenzy of insane killing that leaves a heap of corpses on the stage--not only Tamora, Titus and Saturninus, but also Lavinia and the remains of Chiron and Demetrius. The effect is shocking but casts a light on the indifference to human life which is apparent from the very start of the play.