Frangipani trees do not require regular pruning. If a branch is inconveniently placed, it can be removed during winter while the tree is dormant. Frangipani trees will bleed sap if pruned during a growth period. Do not shorten branches of frangipani trees, or dieback will occur. On all trees and shrubs, a thickening of the stem forms where the new branch begins to grow. This is called the ‘collar’, or ‘wrinkle’. On frangipani trees, remove the entire branch, cutting through the branch at the outer edge of the collar. If you remove the branch flush with the trunk, scar tissue that forms will damage the phloem layer that transports carbohydrates in plants.
If you want to take cuttings from your frangipani, the best time to do this is at the end of winter. Remove a lateral branch for each cutting, as described above. Keep these in a dry spot, out of direct sunlight, for a couple of weeks to allow the cut end to form scar tissue. If you take the cuttings during Last Quarter phase, they should be ready for potting during the following Full Moon phase.
For each cutting, half fill a 20 cm pot (with plenty of holes in the base) with well-washed coarse sand that has a little moistened coco peat or compost mixed through it to help keep the mixture damp. Avoid using a normal potting mix for frangipani cuttings because they will rot if the mixture stays too moist. Anchor the cutting in the sandy mix, and gradually fill the pot with the same mix, you may need a short stake to keep it upright. If the cutting is very large (1.5 m), you will need a larger pot with plenty of drainage holes and 3 stakes to support the cutting. Gardening Australia has an excellent video of this method: https://www.abc.net.au/gardening/factsheets/staking-a-tree/9493998
I find strips cut across old T-shirts or men’s singlets make could flexible plant ties. Gently water the mix to settle it around the cutting. A drink of seaweed extract tea can help stimulate root growth. Place potted cuttings in a warm, well-lit area, out of direct sunlight, and keep the cutting mix just damp. During spring, when white roots appear at the holes near the base of the pot, your cutting is ready for transplanting.
Frangipani roots are very brittle, and may snap if you tip the plant out of the pot. Gently remove the mix from the top half of the pot, and then use a hose to gently wash the rest of the sand away. Transplant into well-drained soil in a sunny position. Mature frangipanis are quite drought-tolerant but young plants will require a weekly watering in dry weather until they are making good growth. Organic mulch is beneficial if it is kept well clear of the trunk. These trees only require a light application of complete organic fertiliser in spring (but not at planting time).