This is such an interesting question, and I think I want to respond to it by focussing on Twelfth Night by Shakespeare. This to me is a perfect example of the "dark side" of comedy. The character of Malvolio and the comeuppance he receives thanks to Sir Toby and Maria is excessive to say the least and in the worst possible light, downright cruel. Note how Malvolio at the end shouts out his challenge against the happy ending that we all expect and applaud of a comedy, and his words, "I'll be reveng'd on the whole pack of you!", strike a deliberately discordant tone that we then go on to clap as the play ends. Shakespeare seems to suggest that we can laugh too much and the dividing line between comedy and tragedy perhaps isn't that firm or fixed after all.
Some satire is very biting. Saturday Night Live, for example, has on a number of occasions brutally ridiculed presidents, presidential candidates, celebrities, and public figures of all types. One memorable "roast" of a singer was the parody of Joe Cocker by John Belushi. While SNL's satiric portrayals are usually funny, some are, indeed, rather cruel.
No. Comedy, by definition, is meant for laughter and fun. In most comedies, humanity is forced to look at its own foibles and weaknesses--thus, in this way, it could be interpreted as cruel. In reality, it is more like satire, and it meant to get people to recognize these weaknesses in order to improve themselves and therefore, improve the world in which we live. This is one reason comedians like Carlos Mencia are so popular--he points out everyone's weaknesses and the stereotypes that are present in order to encourage awareness and improvement.
Comedy by definition is not cruel. It can, however, be used for numerous other purposes. When comedy is used for other purposes, it ceases to be comedy and becomes satire, or irony, or absurdity, etc.
Thus, my answer is, no, comedy is not cruel.
Take Swift's "A Modest Proposal." It is a classic, ironic, satirical essay. It is also extremely funny. But no one would call it a comedic essay. It is not. It has a different purpose than to entertain and make people laugh. But it uses comedy to satirize.
By definition comedy entertains and makes people laugh. It is not cruel. But it can be used to satirize, etc.
By the way, comedy and irony, for instance, are closely related, yet different. The essence of both comedy and irony is surprise/opposition. You get the opposite of what you expect. The opposition in comedy makes you laugh. The opposition in irony serves other purposes.
Comedy can be cruel but it also depends on the attitude of the viewer or listener and their sense of humor. The purpose of plays and literature is to entertain the reader or audience. If that person has a good sense of humor then they may not view it as being cruel, simply funny.
On a more serious note, sometimes cruelty in plays or literature is truth. The author is attempting to add humor to events that make us feel sad or upset. We do live in a world which contains many cruel elements and plays or literature are usually reflections of feelings or emotions that the author is feeling.
Cruelty means different things to different people so what one may deem as cruel, another may not.
In my opinion, it can be cruel but it does not really have to be cruel. I am thinking that maybe you can differentiate between farce, which does not seem to have to be cruel, and other kinds of comedy, which might.
I'm thinking about the difference between A Midsummer Night's Dream and The Taming of the Shrew here. To me, it seems that the first of these is not cruel while the second one is.
In Dream the humor comes more from the weirdness of the situations and the intervention of Puck. It does not seem to make fun of people, for the most part. By contrast, the humor in Shrew is much more focused at certain people -- just about every joke has a butt to it. That kind of humor is potentially cruel because it is always making fun of someone.
Most certainly comedy by definition is something amusing funny or comic. But what is amusing or funny for some may not be all that amusing or funny for others. Particularly when the laughter is at the expense of someone else.
Comedy and laughter can be very cruel and very dangerous also. One of the main contributor the the war between Pandavas and Kauravas which is described in the ancient epic Mahabharata, was Draupadi, wife of Pandavas laughing at Kauravas.