There are actually three examples of irony going on with Cassius’ death.
First of all, look at why Cassius decides to kill himself. During the battle, the armies of Cassius and Brutus are not in direct contact with one another. Cassius is fighting Antony’s army, and Brutus is fighting Octavius’ army. At one point, Cassius asks one of his men to tell him how the battle is going for Brutus. The man mistakenly believes that Brutus has been defeated and captured, and tells Cassius so. Cassius says:
O, coward that I am, to live so long
To see my best friend ta’en before my face!
A moment later, Cassius, believing he is doomed to defeat and then imprisonment, tells his servant to kill him with his own sword.
Another irony is that the battle that leads to Cassius death actually occurs on Cassius’ birthday.
The third irony is that the sword that kills Cassius (his own sword), is the same sword he used to kill Caesar, which leads Cassius to say:
Caesar, thou art revenged,
Even with this sword that kill'd thee.