First off, a lot of that is exaggerated. The Europeans hardly set up "death camps" or went on random killing sprees when they landed in the Americas. They simply didn't have the numbers, by and large.
The biggest killer was disease. Frankly, those diseases were so virulent, and spread so fast, that the vast majority of the native population probably died of second, third, or fourth hand exposure without ever having seen a single European person in the flesh.
We know for fact, for example, that the native civilizations living along the Mississippi river went all but extinct long before European explorers ever arrived, because all we found when did eventually explore these areas were a few scattered tribes, and the ruins that the larger civilizations those tribes once belonged to had left behind in the pandemic's aftermath.
Hell! Even where the infamous Cortez is concerned, all he really did was help the native city states in the area he explored to rebel against their brutal Aztec overlords in return for oaths of fealty to Spain.
Now, granted, due to the effects of disease, economic ignorance, and bigotry, the Spaniards did sort of botch their governorship of the area afterwards. However, even then, it was never really "wholesale slaughter" so much as simple incompetence.