Gutta percha seems to be a variety of latex, related to but less elastic than caoutchouc (which I mention only because I love the name). Gutta percha comes from the sap of a Malaysian tree; one source says Palaquium gutta¹, another says Isonandra gutta²; in any case, the harvesting process kills the tree. It was first brought to European notice in 1843. "Percha" may mean Sumatra; then again, it may mean "a rag or remnant"². "Gutta" may be an English corruption of the Maylay "getah", meaning "sap".
¹
http://www.bartleby.com/65/gu/guttaper.html
²
http://www.bibliomania.com/Reference/HobsonJobson/data/403.html#gutta--percha