I have had some success with cuttings from passion vine. Use some light soil and take green tip cuttings with a node. Keep them moist and covered with a plastic bag or cut off soda bottle top. I had two out of three root last time I did this.

You might also try dipping the base of the cuttings in a powdered rooting hormone.If you punch a hole in the moist soil with a pencil then insert the powdered cutting into the hole you can push the soil up around the stem. That will keep the powder on the stem which is supposed to help roots form. Be sure to keep the closed container out of the sun so it won't cook your cuttings. Hope it works for you. Your vine has beautiful flowers. Good luck!