What is ironic about the way Beowulf kills Grendel's mother?

Like Grendel, Grendel's mother seems immune to the sword. He cannot cut her, so he uses his strength to wrestle her to the ground.... note, their wrestling match ends in a draw. None-the-less, Beowulf manages to pick up a large sword, which he uses to cut off her head. This is ironic because his sword hadn't worked earlier.