In Fahrenheit 451, the death of Captain Beatty in Part Three is ironic for a couple of reasons. Firstly, it is ironic that a man who defends the fireman system should be killed by it. Back in Part One, for example, Beatty made a speech to Montag in which he argued that the fireman system protected minorities and made people happy because they are not "stuffed with facts." It is ironic, then, that Beatty, a man who has been a part of this system for so long, should die by it. 

Secondly, at the time of his death, it is ironic that Beatty should call Montag a "silly damn snob" for quoting literature when he then goes on to quote Shakespeare:

"There is no terror, Cassius, in your threats, for I am arm'd so strong in honesty that they pass by me as an idle wind, which I respect not!"

In doing this, Beatty berates Montag for an action that he himself carries out and which is partly responsible for his own demise. Had he not verbally attacked Montag, for instance, there is a chance that Montag would never have killed him. But Beatty's attack on Montag was deliberate: he wanted to be killed that night and this reveals another irony in his death. Namely, that a man who calls the firemen "The Happiness Boys" should be so miserable that he has suicidal tendencies.