Yes, you can make new trees from cuttings. Plant pieces cut from a parent plant and rooted to form new plants are called cuttings. Explained further below. New plants formed from cuttings have the same characteristics as the parent plant. The process of rooting cuttings is simple and inexpensive. There are different types of cuttings called, softwood, semi-hardwood, and hardwood cuttings. Different woody plants such as deciduous, or evergreen trees require appropriate propagation techniques. Also, the best cuttings are selected  from vigorous, healthy wood, preferably from the upper part of the plant. Avoid excessively vigorous shoots and weak, spindly growth which will produce poor results. See complete how to take cuttings in the link below: http://extension.missouri.edu/publications/DisplayPrinterFriendlyPub.aspx?P=G6970

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NYBG Plant Information Service