You seem to be avoiding the saber-toothed tigers and the woolly mammoths. They did NOT go extinct as a result of a meteor impact. So, how do you explain individual species extinctions? If they were properly designed...
I'm not "avoiding" them -- it's just that you're constructing a strawman, and I saw no point in addressing it. I see that it's necessary to provide further detail on the matter. The strawman is in the way you define the motivation and goals of the putative designer. In essence, you're saying that the only possible design agent is an omniscient designer who would never design anything that would go extinct.
However, we know from our own experience that we often design things to serve some singular purpose, and we forget about the thing once we no longer have a use for it, and thus we know that there is no strict requirement for a designer to be either omniscient, nor for him to "design for forever."
In terms of the sabertooth cats themselves, the achievements of the modern biotech industry -- not to mention the practice of selectively breeding animals to achieve certain desirable traits -- seem to indicate that there is no intrinsic barrier to an intelligent breeder deciding to create a breed of large cat with long teeth. I'm not saying that this did occur, but there is no technical reason why it could not have happened, either. Indeed, humans have frequently done very similar things.
The most recent theory I've seen for the extinction of the Woolly Mammoth is that they were done in by a combination of human predation and disease. The extinction of the saber-toothed cats would likely have followed as a consequence of the loss of their primary food source -- but that has nothing to do with how they got their long teeth in the first place.