In their battle
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He cuts Grendel's arm off.
He rips off Grendel's arm with his bare hands/
He rips off his arm and places it in Herot. Grendel runs home and laters dies in his lair but his mother goes back to Herot to kill and gets away until Beowulf goes to her lair and cuts off her head. He does find Grendel, however he is already dead by that point.