First of all, a mammoth revived in this way would obviously resurrect no microbes with it directly from the past.
Second, if there were some fearsome microbe lurking around in mammoths then it would've thawed along with the mammoths when taken out of the permafrost (but surely in a degraded state). Researchers have actually searched for such things.
Third, a microbe that is so non-adaptive that it hasn't had a host since mammoths went extinct is not likely to mutate into anything that threatens humans. Actually, such a microbe is almost certainly extinct itself.
Fourth, any microbe that infected mammoth that was likely to jump the interspecies barrier would almost certainly be hanging out at the very least in elephants today.
Finally, the population of mammoth is not likely to be large enough to sustain much of a population or much evolution, as microbes go. It would be decades, at the very least, before it was and that would be plenty of time to detect any fearsome, novel microbes and our own medical tech would advance dramatically in that time (esp. broad-spectrum antiviral medicine).
Beware, foolish mortal! You tinker with forbidden knowledge!
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