They don't grow from cuttings. Propagation is by division. Dig up the clump and carefully pull away growing points with tubers attached and pot up. Replant the original clump.

There are several excellent videos on YouTube. I use a bread knife to cut between fans, and keep 3-4 fans together. Single fans take a long time to recover and start flowering again, but need dividing less often. They need at least 6 weeks before the first frost to settle in. If you get proliferations - growth on the flower stalks - they will be the same as the parent plant. Just replant everything with the crown at soil level to prevent rot.

Thank you very much for replying to my question on Day Lilies .