The earliest appearance of a superstrong filament that can cut through things seems to be Theodore Sturgeon's "molecularly condensed fibre" in "The Incubi of Parallel X," Planet Stories September 1951:
Garth took pity on him — he was obviously about to burst with curiosity. He held up the thread. "Break off a piece for me, Bronze boy."
Bronze took the end of the thread, wrapped it around his fists, and — "Wait!" laughed Garth.
He picked up two heavy pieces of tree branch, unwound the thread from the big unresisting fists, and took a couple of turns of the thread around each piece of wood, leaving about six inches of thread between them. "Now try it," he said. "Grip the wood, not the thread."
Puzzled, Bronze grasped the two pieces of wood and pulled. The thread went taut with a musical twang which rose in pitch as Bronze pulled. A look of utter amazement crossed his broad face. He relaxed, turned the two pieces of wood so that he wound up more thread and had only two inches between them. He set his back against a tree, knotted his jaw, and, with his great hands close to his chest, began to pull. His triceps swelled until the stretched skin shone. His body moved visibly away from the tree that he leaned against as his scapular muscles bunched and crawled.
There was a muffled crackling from his shoulders, and Garth stepped forward in alarm. Then one of the pieces of wood gave. The thread sliced through it like a scythe through a stand of wheat, and Bronze stood gasping, staring foolishly at the cleancut stub of branch in his hand. The thread fell away, unstretched, unbroken.
"I gave you the wood," Garth grinned, "because it would've sliced through your paws."
"What Ffanx stuff is that?" gasped Bronze.
"That isn't Ffanx stuff; it's strictly human, molecularly condensed fibre spun under massive ion bombardment, if that makes any never mind to you. It has linear cohesion in the order of six tons test and eight and a half tons breaking strain. And it has no rotary cohesion at all."
You can read the story at the Internet Archive.