why the supply voltage of dc motor decreases when the motor load increases?
The battery also has internal resistance.  As the motor draws more current to accelerate and run at a higher speed, the increased current draw will create a larger voltage drop across the battery's internal resistance.  The result is voltage droop.  

Discharge rate would be measured in units of watts anyway, which is volts times amps.  The increase in current will more than offset the drop in voltage so that ultimately you are drawing more power, just at a lower voltage.