They've found more than just bones and fragments. They have found whole mammoths frozen/preserved, however sometimes they are exposed to the elements for a week before they are properly moved to a laboratory.
Not sure if there would be "living cells" in them. Talk about freezer burn.
The trick is to find the mammoth still buried (remote imaging?) in the permafrost and cut out the whole block of Earth, take it where it can reasonably be worked on, and clean away the soil without damaging or defrosting the flesh.
The flash-frozen layer of the mammoth is on the outside, and at least some decomposition from residual body heat is likely in the innards. OTOH, the most famous recovery was of stomach contents of one of the first mammoths ever found and examined by scientists.
The london historical society fond one in the 1930’s, I think - they had a BBQ.