What would happen to a skyscraper building if a tornado hit it?

The first thing that would happen is the rubble that the tornado brings with it would break the windows. This would cause major damage to the contents of the floors. Worst case, if the wind speed was high enough and the building structure was weak enough then the building could collapse.

Depends on the size and intensity of the tornado. It could do anything from break the windows to level the building.