My latin textbook mentions the use of irony by some writers, among them Martialis who wrote:
"Nollem accidisset hoc tibi, Saleiane"
"I wouldn't want that this happenend to you, Saleianus"
This is irony, as Martialis knew for sure Saleianus was actually happy with the event, the death of his very rich wife.
Do you mean the origin of the word "sarcasm" itself? Or sarcasm as a concept, which is perhaps as old as language? Even certain (animal) behaviors can be sarcastic.
An example from a previous thread:
Richard Lee pioneered the study of African tribespeople, namely the Ju'/Hoansi (better known as African bushmen, they are hunter-gatherers, live in nomadic tribes, and speak the crazy click-language like in The Gods Must Be Crazy). He lived with the tribespeople and learned their language, and in one of his ethnographies, he describes at length how incredibly sarcastic the people are. For example, someone would come back with something they killed (which they share with the whole tribe) and everyone else would say stuff like "It is so bony, it will hardly feed one person, look at that worthless sack of skin," etc and belittle the hunter in general-- especially when it was a nice, big animal or impressive kill. They use sarcasm to keep everyone in check. Because they have no government or hierarchy (not even a chief), they try to keep it all egalitarian by not letting anyone's achievements go to their head. Everyone is equal. They tease and satirize each other all the time to maintain that equality. Lee had a hard time because, also being new to the language, he almost never knew if they were being serious and would get frustrated when everyone would be laughing at him. Also, they celebrate Christmas, and what they call it pretty much translates to "praise of the birth of the white man's god-chief." Awesome.
I recommend reading this post by the linguist Mark Liberman.
Sarcasm in the sense of bitter or cutting remarks must obviously predate human history, and there are many fine examples in the Iliad, one of the earliest written works, such as Achilles' speech to Agamemnon:
Why, you shameless schemer, why should any Achaean leap to obey your orders to march or wage war? No quarrel with Trojan spearmen brought me here to fight: they have done me no wrong. ... No, for your pleasure, you shameless cur!
... and so forth.
Sarcasm in the sense of irony has also been claimed to be a human universal, as in this passage cited in the Liberman blog:
Verbal irony is universal and appears to arise spontaneously, without being taught or learned.
Sarcasm shows up in the Book of Exodus: "Did you lead us out here to die in the desert because there weren't enough graves in Egypt?" - see, it's funny because the pyramids are giant tombs, Egypt is famously full of graves.