While eucalyptus trees are commonly grown from seed, it is possible to propagate eucalyptus trees from cuttings, although the success rate of rooting cuttings is only about 5 percent. Still, it's worth a shot if you have trees nearby with plenty of potential cuttings. To improve your chances, take cuttings in the spring or early summer, when the new growth on the plant is still relatively immature and thus more likely to "take" in its transported location.
Snip a cutting off the eucalyptus tree with garden clippers, making sure you make a smooth, clean cut. Select only a shoot of new growth, about a foot in length.
Prepare a pot of potting soil. Fill a pot with a layer of gravel at the bottom to promote good drainage, and then fill in the rest with potting soil. Water thoroughly.
Treat the cutting with a root hormone to stimulate growth. Root hormones are available under various brand names, including Dip 'N Grow.
Stick the cutting into the soil to a depth of about three inches. Cuttings take four to six weeks to develop roots, but, again, keep in mind the success rate is low and you might have to try several times before you succeed.