Beowulf and Grendel had a horrid final battle in which each put the most of each in order to defeat the other. What we do know is that right on the most poignant moment in the story Beowulf saw a sword all of a sudden which is described as:
An old giantish sword with firm edges, An honour of warriors, it was the choicest weapon.....
From what we can infer, that sword was an ancient and powerful symbol of ultimate defeat which he took in a very heroic moment. With all the might in his heart he grabbed such sword and struck her through the neck, breaking her bones and decapitating her with it. Therefore, Grendel's mother was beheaded by a old gigantic sword.