I think there are at least a couple instances in the Bible where some wit is shown, although it tends to get lost in translation.
In 1 Kings 18, Elijah straight up taunts the prophets of Baal because their rituals weren't causing Baal to miraculously set an altar on fire. Elijah proceeds to say, “Shout louder! Surely he is a god! Perhaps he is deep in thought, or busy, or traveling. Maybe he is sleeping and must be awakened.” What's missed is that the "busy" part is actually a euphemism for using the bathroom. Then, just to really shame the false prophets, Elijah has the altar DRENCHED and then God epicly shows off with fire from heaven.
John 6 amuses me. Jesus drives these people nuts. In the previous chapter he had MIRACULOUSLY FED THEM and they come asking for a sign for his divinity. Then he proceeds to speak in metaphor calling for them to perform cannibalism and vampirism in order to be saved (no offense to Catholics; I dunno if it's true, but I've heard that Catholics believe the disciples literally ate his flesh and drank his blood during the Last Supper), basically enraging them. And I chuckle at their dullness.
Jeremiah 36:17-18 has a bit of dry wit in it:
Then they asked Baruch, “Tell us, how did you come to write all this? Did Jeremiah dictate it?”
“Yes,” Baruch replied, “he dictated all these words to me, and I wrote them in ink on the scroll.”
Well derp, no duh. Interestingly enough, Baruch's name's root word means "blessing." You might say he was blessed with a quick wit, although some of the people might not have considered it much of a blessing!
When you think about it though, the Bible was predominantly written by Jews - a people renown for their sarcastic wit.