Symbolism, Imagery, Allegory
You probably noticed all the lopped-off body parts rolling around on stage in Titus Andronicus (there are six dismembered body parts total). You may have also noticed some metaphorical references to "hands," "limbs," and "heads." So what's the deal? Is this Shakespeare's idea of a sick joke? Well, sort of.
The first thing to know is that Titus Andronicus is a part of a popular 16th century genre called "revenge tragedy," where blood, guts, and mutilated bodies are par for the course. (Check out "Genre" if you want to know more about this.)
There's also a political metaphor at work in the play. Every time a body is hacked up, we're reminded that Rome's "body politic" has also been torn apart by civil strife. FYI – the "body politic" is a political concept that sees rulers (kings, emperors, etc.) as "heads" of state, while citizens and subjects are considered body parts. The body politic concept appears early on in the play when Titus is elected emperor. Marcus urges him to accept the job and "help to set a head on headless Rome" (1.1.3).
Well, Titus doesn't take the job, and we're led to believe that his refusal to lead is at least partially responsible for all the violence that eventually rips Rome and its citizens apart (literally and figuratively).
At the play's end, Marcus, who wants to repair and unify Rome under a new ruler, says "O, let me teach you how to knit again [...] / These broken limbs again into one body" (5.3.2). Marcus is speaking metaphorically, but the playwright's sick joke here is that the stage is actually littered with "broken" bodies.