Dear Student ,
No fuse must have a low resistance. Whenever there is an excessive current the fuse must blow. Now if there is a regular amount of current it should pass it. With a high resistance it would fail to do so. On the other hand the heat generated in a conductor is given by I2R. So if I goes high R should have such a value that the heat generated will be enough to melt the wire. The resistance of a fuse wire may vary but usually it has a low resistance.
A fuse works on the principle of heating effect of current. If a high current is passed through the wire, the fuse wire will get heated up and melt, thus breaking the circuit and preventing damage to the appliance.
Regards