Chapter twelve of Beowulf describes the battle between Beowulf and Grendel. In this battle, Grendel realizes that he is outmatched by Beowulf's strength. Unfortunately, he realizes this too late and departs Heorot without one of his arms. Grendel, "sick unto his death," returns to his den in the dark recesses of the moors.
Later, in chapter twenty-three, Beowulf again faces Grendel. This time, Grendel proves to be of no worry. Grendel has died from the injuries Beowulf gave him during their battle in Heorot. Regardless of the lack of life in Grendel, Beowulf, wishing to "promptly repay" him for all of the hardships he put on Hrothgar, split the body of Grendel open and removed his head.
See chapter 12