Why does time dilation occur due to the velocity of a moving body, according to SR?
This is a very broad question. I would recommend starting with a basic reference (something like http://en.wikipedia.org/wiki/Time_dilation), and then come back with specific questions.
The whole of special relativity is to construct covariant theories under Lorentz transformations and the dynamics part arises directly from Lorentz transformation itself. The reason is that the classical theory of electromagnetism is a covariant theory in Lorentz group and thus that the speed of light is invariant. So you could say that the reason behind is famous statement of the principle that speed of light is invariant...but I don't know at which level you are asking about.
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