In scene (3.1) Aaron promises Titus two of his sons returned alive if he or one of his family will give the Emperor a hand. Literally. The request is definitely not funny- it's pointless and cruel- but the argument about whose hand will go is easily played for a laugh.
The latter half of Act 3, Scene 2:
Titus: "What dost thou strike at, Marcus, with thy knife?"
Marcus: "At that that I have killed, my lord- a fly."
Titus: "Out on thee, murderer! ...Poor harmless fly, that with his pretty buzzing melody came here to make us merry, and you have killed him!"
Then, when Marcus says that the fly reminded him of Aaron the Moor, Tamora's vicious lover, he stabs the already-dead insect multiple times. And then lampshades the impassioned foolishness of it all.
The above sequence was added some years after the play was originally written, and it has always seemed to me to be a tongue-in-cheek jibe by the author at the sensationalism of his early work.