He cuts off his head to keep as a trophy.
In the EPIC of Beowulf, she was slain by a sword made for a giant and sliced her head clean off in one clean cut.
Beowulf cuts off Grendel's head to end the creature's reign of terror on Heorot and the people of Hrothgar's kingdom. It symbolizes Beowulf's victory over evil and his heroic triumph in vanquishing this monstrous threat.
Yes, Beowulf does fight Grendels mother, they fight in her lair. He chops off her head.
Grendels arm If its after the fight with Grendel's Mother then he took Grendel's head, the sword-hilt of the sword he used to slay Grendel's mother and cut off Grendel's head, and of course Hrunting the sword he originally brought to slay Grendel's Mother which was ineffective against her tough hide.
Considering that Beowulf was able to defeat Grendel without any weapons or armor, Beowulf is much stronger. He ripped Grendel's arm off in the fight and Grendel fled.Also, Beowulf was very young at the time.
grendel gets away, but he is fatally wounded and goes to his den to die.
Beowulf cut grendel's arm off and saved it as a trophey
Beowulf gets hold of Grendel arms. Grendel cant handle the pain and wants to return back to its den. But Beowulfs immence hands rip of Grendels and Beowulf slauters Beowulf.
After Beowulf cut off Grendel's arm, Grendel fled back to his lair where he eventually succumbed to his injuries and died.
He is attacked by Beowulf and Beowulf tears his arm off and injures him very badly. Grendel then escapes, but is so badly wounded that he dies, and Beowulf is seen as a hero. Later, Grendels mother goes to avenge Grendel's death.
Grendel's mom tried to kill Beowulf for her son's vengeance. This was a tougher battle for Beowulf because his sword wasn't able to hurt her mother so he use his fist and gradually found a mystic sword and cut her head off.