Why did humans develop the "sense of humour"? Speaking from the point of view of evolutionary psychology, is there any research that demonstrates why a 'sense of humor' may be a part of our mental mechanisms?

Does research show that it is a way to quickly decrease stress levels?
Interestingly, the same question you asked has been asked since quite some time:

The Act of Creation, 1964 - Arthur Koestler


  What is the survival value of the involuntary, simultaneous contraction of fifteen facial muscles associated with certain noises
  which are often irrepressible? Laughter is a reflex, but unique in
  that it serves no apparent biological purpose; one might call it a
  luxury reflex. Its only utilitarian function, as far as one can see,
  is to provide temporary relief from utilitarian pressures. On the
  evolutionary level where laughter arises, an element of frivolity
  seems to creep into a humorless universe governed by the laws of
  thermodynamics and the survival of the fittest.


Firstly, like all other narratives built by evolutionary psychologists, it is difficult to back up speculations with empirical evidence. Since we are going back far back into the evolutionary history of homo sapiens, we will be dealing with what I would call "well-informed speculation".

Quoted from The Mating Mind (2001) by Geoffrey Miller.


  To traditional evolutionary psychologists, human abilities like music,
  humor, and creativity do not look like adaptations because they look
  too variable, too heritable, too wasteful, and not very modular. But
  these are precisely the features we should expect of fitness
  indicators. If a human mental trait shows large individual
  differences, high heritability, high condition-dependence, high costs,
  and high correlations with other mental and physical abilities, then
  it may have evolved through sexual selection as a fitness indicator.
  (pg. 132-133)


Sexual Selection

Notice that he also mentioned your speculation about decreased stress levels:


  Some theories of humor have proposed that laughter evolved to promote
  group bonding, discharge nervous tension, or keep us healthy. The
  more laughter the better. Such theories predict that we should laugh
  at any joke, however stupid, however many times we have heard it
  before, yet we do not. A good sense of humor means a discriminating
  sense of humor, not a hyena-like shriek at every repetitive pratfall.
  Such discrimination is easy to understand if our sense of humor
  evolved in the service of sexual choice, to assess the joke-telling
  ability of others.


Furthermore, I recommend that you read this review of Robert Mankoff of “Inside Jokes”: The Hidden Side of Humor. (2011) and of course the book itself. It sheds a strong light onto your question.



Sources:

Matthew M. Hurley, Daniel C. Dennett, and Reginald B. Adams Jr., Inside Jokes: Using Humor to Reverse-Engineer the Mind. MIT Press, 2011, 376 pp., ISBN-13: 978-0262015820

Koestler, Arthur. 1964. The Act of Creation, Penguin Books, New York

Miller, G. (2000), The Mating Mind: How Sexual Choice Shaped the Evolution of Human Nature, London: Heineman, ISBN 0-434-00741-2 (also Doubleday; ISBN 0-385-49516-1)