The Roman writer Juvenal (1st-2nd centuries AD) uses sarcasm in his Satires. Personally, I think he is quite intelligent and funny, although he can be biting. Think of an ancient Jon Stewart, but slightly more cruel and dirty-minded.
Here is one example of his sarcasm which came to mind in Satires VI.44-48:
...he seeks a wife with traditional virtues?
O, good doctor, relieve the pressure on that swollen vein!
What a fastidious man! Go prostrate yourself in worship
At the Tarpeian shrine, go sacrifice a gilded heifer to Juno,
If you should happen to find a woman whose life is chaste.
There are other Roman writers that used sarcasm, too. Martial might fit, but I can't recall anything to quote off the top of my head.
He won't go down as ancient (being 11th C) but I've always particularly enjoyed Su Shi's snide reflection on the state of the Chinese bureaucracy and its treatment of him:
All people wish their children to be brilliant,
But I have suffered from "brilliance" all my life.
May you, my son, grow up dumb and stupid,
And, free from calamities, end up as premier!
For an earlier example, it maybe lacks the irony we usually associate with sarcasm but I can appreciate how Empedocles (5th C BC) was suitably cutting when he remarked on the decadence of his home town by noting that:
The people of Akragas build as though they would live forever and eat as though they would die tomorrow.
(Which is a modern paraphrasing of the original, "The Agrigentines live delicately as if tomorrow they would die but they build their houses well as if they thought they would live for ever."")
How aware are you of Loconism? The idea that you punch the message home with as few words as possible allowed for a lot of cold, Clint Eastwood style, sarcasm as opposed to the more camp, Comic Book Guy type.
I guess the most famous example is mention in 300. When Dianekes is told that the Persian archers' arrows would block out the sun, he responds by saying "then we fight in the shade”.
"when the Barbarians discharged their arrows they obscured the light of the sun by the multitude of the arrows, so great was the number of their host, he was not dismayed by this, but making small account of the number of the Medes, he said that their guest from Trachis brought them very good news, for if the Medes obscured the light of the sun, the battle against them would be in the shade and not in the sun."
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