The expression “to cut one’s eyeteeth” means to acquire wisdom; to learn the ways of the world.
An eyetooth is a canine tooth, the third from the center in the upper jaw.
The expression is somewhat literal, for the implication is that by the time a person has got his permanent set of canine teeth, has reached the age of twelve or fourteen, he has passed out of babyhood and has reached years of discretion.
This wording of the saying appears to have originated in the United States, first recorded in 1870 by the essayist, Ralph Waldo Emerson, though undoubtedly long in use before that date. The British version, dating to the early eighteenth century, is “to have one’s eyeteeth” or “to have one’s eyeteeth about one.”
The usage differs slightly, carrying the implication of alertness against chicanery; that is, to use one’s knowledge and experience in one’s dealings.