"it is interesting to note that those same noble savages killed off the mammoth, mastodon, etc."

There is still a debate going among archaeologists as to the proximate cause of the extinctions--climate change or overhunting.  See one discussion:  http://www.sfu.ca/archaeology/museum/mammoths/extinct.htm

Most likely it was a combination of the two, but there are good arguments made on both sides.  The so-called "savages" lived with the same pressures we do--finding enough resources to survive and reproduce.  In an environment where there was an abundance of other game, I doubt there was much pressure to conserve one species.  Mammoth and mastodon were preferred because there was a lot of return on your investment of energy.  Once they were gone, people switched to other sources but probably not without difficulty.  In general (there are always exceptions of course), tribal hunter/gatherers evolved ways of living sustainably in their environments, including keeping their population sizes stable through infanticide if necessary.  While that statement might be construed as an argument for the validity of:
"Our ancestors were just as cut-throat as us" there are also examples of hunter/gatherer cultures that are much more cooperative and non-agressive than we are.  Google the Kung people of the Kalahari, or the Mbuti people of the Forest in Africa.  There are also the Yanomamo in the Amazon, however.  My point is that it's not necessarily true that humans are by nature wasteful or "cut-throat".  Culture has much more to do with it and that is something we can change.  Given the dwindling supply of the resources that keep our culture going, IMO we are definitely going to have to change and adapt in order to survive.