Question

How does deforestation lead to frequent floods and droughts?

Answer 1

When the forest trees are cut down, then the lesser number of trees put less water vapour into atmosphere through transpiration. Since, less water vapour is put into the atmosphere, there is less rainfall in that area.

When there is less rainfall in an area, then less water percolates into the ground. Due to this, the groundwater level also gets lowered. The shortage of surface water (in ponds, lakes, etc) and groundwater due to persistent low rainfall in an area can lead to droughts.
Deforestation also leads to a decrease in the water holding capacity of the soil. When trees are cut down there are no roots for absorbing rainwater. Thus, the movement of water from the soil surface into the ground is reduced.
So, there are floods. Soil erosion caused by cutting of trees also contributes to floods. The eroded soil keeps on collecting river bed, decreasing its depth. This leads to overflow when heavy rains occur.