The gnomish woodcutter is a vehicle for the fragile gnomes. It has high armour and is difficult to defeat. It typically carries a gnome, without whom it is incapable of defending itself. Once its passenger is defeated, it can be used to practice combat skills.
It is best attacked by using ranged weapons to attack and kill the gnome. After that, it can be destroyed by perseverance. There are a few ways to beat it. One is to get your pet to kill the gnome, making is nonfunctional. You could also use a wand a lightning to kill the gnome, throw a potion of acid at the Gnomish woodcutter (the acid will usually kill the gnome) or use the ceiling as a mirror for a magic missile.