The Mongol invasion of China did not happen in one go. Over a relativly long period of time they attacked again and again and eventually defeated the last of the remaining dynasties.
There first campains agains the Xi Xia and the Jin where very destructive, lots of burning and raiding. In the Jin campain the where not jet able to capture large citys so the went for strategic raiding.
Its is estimated that the north of china droped in population from 100 to 60 million people. How many people where killed and how many fleed is not clear. It is however clear that there was a mass flight to southern china where the Song Dynastie still held there lands.
The conquest of the South (the Song) was destructive too but not in the same scall as most of there other conquest where. By now the mongols (or rather Kublai Khan) had learned that a soft touch can also help you in the long run. Kublai had learned in his war with his brother how usful the resources of china are and that controlling and taxing will be easier then raiding and destroying. So Kublai to the outside presented himself as a classical emporer but mongol childern where still born in a yurt.
So never underestimate the destruction of a mongol invasion but south china was not as bad as Jin or Khwarezmian Empire.
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