The motor at first worked well but didn't respond to the potentiometer. Anyway, One day after that, I powered the circuit again but the driver got so hot and the motor held at its position with some noise. So, I disconnected it and tried again but the driver wasn't working (I tried the stepper alone and it worked). So, what could be the reason? Can unfiltered power supply destroy such a circuit? (I connected the circuit as shown but didn't connect any capaitor in my circuit)
Motors behave like inductive loads. Suddenly reducing or interrupting current supply on a motor will generate a voltage spike (called flyback) on it's driving lines. The driver can survive spikes, but not forever. The flyback should be eliminated with a diode. You can read more about it on the Wikipedia.
Note: since you can drive motors in two ways, I suggest adding transient-voltage-suppressor (TVS) diodes (one between A and A\, one between B and B) which can elmininate flyback in both ways.