Now my question is why would Nature cause mutations ?
You talk about nature as though it is a sentient creature, with goals and an agenda. Nature is nothing more than a set of laws that govern the behavior of the universe, and everything that happens conforms to those laws.
Whether or not events happen at random is a question that has not yet been answered; it hinges on our very incomplete understanding of nature's laws, particularly at the scale of elementary particles. But whether or not there is a random component, there is certainly no purpose involved. Nature has no consciousness and is totally indifferent to the fate of her creations--alive or not.
Why has nature caused a mutation if the animals or humans life be so short lived ? it seems such a waste ?
The laws of conservation of matter and energy ensure that nothing is wasted. What you're looking at is the
organization of matter and energy. And one of nature's laws, the Second Law of Thermodynamics, assures us that the organization in the universe will
decrease inexorably over time. The opposite of organization is
entropy, and entropy will continue to increase until there is no organization anywhere in the universe.
Life has been succinctly defined as "a local reversal of entropy," since (arguably) the most important of its defining characteristics is indeed that living things steadily increase their organization throughout their lives, at the expense of disproportionately decreasing the organization of their local environment. For example, a plant grows larger every day, slightly increasing its organization, but only by extracting solar energy from its environment for photosynthesis, reducing the temperature of the environment and causing a much greater
decrease in its organization. A local reversal of entropy results in an overall increase of it.
So to mourn the loss of a life is to resent the increase of entropy and the eventual reduction of the universe to a state of complete disorder.