You're referring to an interpretation of social Darwinism which, other than bearing his name, has very little to do with Charles Darwin or his work. I don't think it was ever something he was actually purported to believe, either. In fact, the original edition of On the Origin of Species never even made use of the now common quip "survival of the fittest." This was something attributed after the fact by English philosopher Herbert Spencer in Principles of Biology, which came five years after the first edition of Darwin's Origin.
Most of this "survival of the fittest" and social Darwinism crap hinges on a misrepresentation of natural selection as we have come to understand it in the modern day. It has absolutely nothing to do with the actual scientific use of the term. Moreover, the theory of evolution and natural selection is much more complex and refined today than it was in the 1800s. Though Darwin's work was legendary for its time -- genetics was not even discovered yet -- he did commit quite a few blunders which have since been corrected and reformed.