I think the term natural selection is sort of a misnomer, makes it easy to misinterpret it as if many are let to die while few are selected. It just happens creatures that with certain traits are more adapted to survive and reproduce (not having tusks in this case), where as some other creatures are not and die. Hence those specific traits tend to be preserved in subsequent generations while the others just didn't survive to reproduce.
And, the extinction events, its not like nature is cruel and killed off most species. As you see in the list of extinctions, the reasons mostly are that the environment (or nature if you will), changed too drastically and quickly that most species couldn't adapt fast enough to survive.