That isnt a normal circuit board 'fuse'. In its normal state it appears to be just a fairly thick single strand wire. It would take quite a lot of current melt it, but perhaps that is their intent.
Of concern is the green resistor above it in your photo. That looks like it has got fairly hot too.
The beep suggests the electronics is working, but the motor drive has blown. This would further indicate that the motor has developed a fault. Worn brushes can causing arcing that produces high current surges.
If it was mine, I'd replace the wire link, but first check out the motor.