Indeed, picture a squirrel cage ,motor which will turn at a fixed rpm according to the mains frequency and number of poles. If this is connected to a centrifugal pump, and you turn down the volts, the power available to turn the pump isn't there any more. This will increase slip, current goes up, disaster results.It very much depends on the type of motor and on the mechanical loading and how that varies with motor speed.
This.What type of motor is it?