How can just random mutations explain mimicry?
/how come these animals (below) show such striking resemblance with their surroundings/

You are looking at the culmination of millions of generations of these insects.  The mutations are random, but only the helpful ones (of all the random ones) produce an advantage for the organism and so persist in the species.   If a random mutation caused an insect to look slightly more like its environment, that insect might do better at avoid predators or catching prey.   Thus it would be more likely to produce offspring which would also have its mutation.  Random mutations that caused an organism to look some other way would not confer any benefit as regards producing more offspring.

In each generation, if there is some random mutation that made the organism more similar to its environment, it could produce better fitness.  The end result, over thousands (even millions) of years, is an organism which looks very much like its environment.  

Fitness is what drives evolution.  Read more at the link if you are interested.  The more offspring I have the more I pass along my DNA and the better my fitness is.  If I have a mutation that lets me have more offspring, that improves my genetic fitness.