The title is of course partially joking — they've got the same mental hardware as everyone else, so presumably humor comes with the package, since it seems reasonably universal — but what I really mean is, what kinds of evidence from archaeology, colonial interactions, etc., do we have about the role of humor in Aztec culture?
I ask this because the majority of the cultural records I have seen of them seem rather, well, humorless — sacrifices and offerings and skulls and the like. They seem to have had an affinity for googly eyes but I imagine they didn't find them as funny as I do (since they put them onto sacrificial knives and the like). What would an Aztec joke have been like? Do we know?
I'm not sure I know of any extant examples of Aztec jokes (maybe with some deep digging), but we certainly see flashes of good humor in the Spanish accounts of Motecuhzoma. Bernal Díaz del Castillo describes him as "very merry in his princely way of speaking," and generally speaks of him as someone charming and graceful, but perhaps our clearest example of good-natured joking about comes from the period when Cortés and Motecuhzoma were basically just hanging out and palling around in Tenochtitlan.
The two men were playing a betting game called totoloque which involved tossing some pellets and "little slabs" in such a manner as to achieve a score, which would then determine wins or losses from your wager. As Díaz del Castillo puts it:
I remember that Pedro de Alvarado was keeping the score for Cortés, and one of his nephews, a great cacique, was marking for Montezuma, and Pedro de Alvarado always marked one point more than Cortés gained, and when Montezuma saw it he said courteously and laughingly that he did not like Tonatio (for so they called Pedro de Alvarado) to keep score for Cortés, because he always made such yxoxol in what he marked, which in their language means to say that he cheated, in that he always marked one point too many. Cortés and all of us soldiers who were on guard at the time, could not restrain our laughter at what the great Montezuma said, because Pedro de Alvarado, although he was so handsome and well mannered, had a mania for excessive talking, and we knew his temperament. (pp. 323-324)
So maybe not a joke with a punchline, but a small peek at someone who knows how to tease and admonish with good humor.
More oblique references can be found through entertainments recounted in early sources. Sahagún, for instance, writes that rulers would be attended by chamberlains who "told him proverbs and pleasantries to pass the time" (p. 29) and they had "jesters who provided them solace and gave them pleasure," (p. 30), though the only specific diversion is an act of juggling a log with their feet. This was apparently a standard enough bit of showmanship to the extent that a juggler in the midst of his act was painted during a visit to the court of King Charles V in 1529.
Nahuas did seem to love their farces though. Torquemada states that merchants at the markets held every fifth day would often put on performances. Hutson (2000) writes that these skits could involve
a merchant dressed as a pustule ridden man complained of his pains and made jokes. In another, two merchants acted as a pair of blind men while another two acted as a pair of bleary-eyed men. The blind and the bleary-eyed then exchanged insults, arousing hearty laughter from their audience. In a third performance, one merchant acted like a mosquito and buzzed, bit flesh, and pronounced various witticisms. Meanwhile, a merchant acting as a dung beetle buried himself in filth. (p. 136)
The Aztecs could also appreciate some biting insult humor as well. There's a passage from Sahagún describing how young women during the festival of Huey Tozoztli would carry ears of dried maize to the temple of Chicomecoatl (the goddess of mature maize). Ostensibly this was a solemn occasion, but apparently these young women were ready with a snappy comeback if some young fellow were to approach them, for
if someone joked [tecamanalhuia] with one of them, they chid him. One said to him:
"He with the occipital tuft of hair can speak! Canst thou talk? Be thou already concerned over how thy tuft of hair will fall off, thou with the little tuft of hair. It is an evil-smelling tuft of hair, it is a stinking tuft of hair. Art thou not just a woman like me? Nowhere hath thy excrement been burned!"
The context being that boys would wear a sort of mullet hairstyle until they achieved their first capture in battle, at which point they could start wearing the distinctive warrior's topknot (or at the very least cut their occipital tuft mullet). The part about burning excrement is less clear, but Anderson and Dibble attribute it to some sort of puberty ceremony. Regardless, all this was clearly meant to be in mocking jest.
Linguistically, the phrase Sahagún used (tecamanalhuia) is derived from camanaloa, which means "to make jokes," and in this specific case the young women are using camanallahtolli (a jest/joke, ridicule) to rebuff the camanalli (jokester, someone who jests) who approached them. There's also the more refined approach indicated via the verb tlahuetzquitia (to entertain someone), which may involve a tlaheutzquitih (someone witty) who makes a tlahuetzquitiliztli (joke).
To close out, we do have a more traditional punchline setup in the primary sources, though it comes from a Spanish friar envisioning a conversation between himself and an old woman on the way to the market. Diego Durán writes about how "inviting, pleasurable, appealing, and gratifying" going to the fifth day markets were, particularly to a certain set of older women who treated it as an almost religious calling. As Durán puts it:
I suspect that if I said to a market woman accustomed to going from market to market: "Look, today is market day in such and such a town. What would you rather do, go from here right to Heaven or to that market?"
I believe this would be her answer: "Allow me to go to the market first, and then I will go to Heaven."
Díaz del Castillo True History of the Conquest of New Spain (1928 abridged trans. AP Maudsley)
Durán Book of the Gods and Rites and the Ancient Calendar (1971 trans. Horcasitas and Heyden)
Hutson 2000 Carnival and Contestation in the Aztec Marketplace Dialectical Anthropology 25
Sahagún General History of the Things of New Spain, Book 8: Kings and Lords (1979 trans. Anderson and Dibble)
Sahagún General History of the Things of New Spain, Book 2: The Ceremonies (1981 trans. Anderson and Dibble)
Look at this forum that has this question previously answered pretty thoroughly. From what I can tell, they definitely did have a sense of humor. From what I can tell, the OP on this one /u/HonorInDefeat was asking basically the same questions and there wasn't much of an answer provided. There was a lack of written evidence to verify most of it but according to /u/Nadarama , they did get a kick out of using word play.
While personally I heard there was a flute found and when sung into it, it was as if the god they placed there was singing (humorous to them according to this article by North Western University). It seems as though the video of it was shut down off the page and I literally cannot find this exact flutes but some similar.
I hope this can help you and definitely check out the old forum posted above.