Pour a small amount of bleach or alcohol onto a cloth to moisten it. Wipe the hand clippers' blades with the moistened cloth. This decontaminates the clippers so disease is not transferred to the Scaevola aemula plant when trimmed.
Prune a stem cutting from the Scaevola aemula plant during the morning hours when the plant is fully hydrated. Trim off a stem that is approximately 6 inches long.
Snip the foliage off the bottom third of the Scaevola aemula stem cutting. Allow the top two to three sets of leaves to remain attached to the cutting. Coat the bottom third of the cutting in rooting hormone, as the hormone helps the cutting quickly develop roots.
Fill a pot that drains with a lightweight seed-starting mix. Moisten the soil with water, allowing it to settle inside the pot. Add additional soil to the pot once it settles if required.
Form a planting hole for the Scaevola aemula cutting by sticking your finger 2 inches into the soil. Stick the hormone-covered end of the cutting into the hole. Cover the hole and firm the soil around the cutting with your fingers.
Water the Scaevola aemula cutting until water runs from the pot's bottom. Set the cutting in a warm, partially sunny area and keep the soil moist through regular watering.