The problem is deer wouldn't go from dumb as rocks to human intelligence in one generation. One particular deer would be a little smarter and a little slower, and he'd be the first in the belly of a wolf. Even if he weren't slower, he wouldn't have any particular advantage over other deer, since his daily routine would still be eat food, avoid wolves, and sleep.
As little as 50k years ago, a mere eyeblink of geologic time, there were giant deer, sloths, sabertoothed this and that, even sabertoothed kangaroos, but they are all gone. Did their niches change? Or did man upset the evolutionary processes by his mere existence?
Most likely man caused natural selection to speed up a bit by eating every single creature you mentioned. Whether or not that is "upset" is up to your interpretation.
The problem is that a deer could have the intelligence of Einstein and it would be useless.
No hands..