I assume that you are asking about the story about George Washington when he was a child and not about any trees that he might have cut down as an adult. If this is the case, the tree that he cut down was a cherry tree. Specifically, it was a cherry tree that his father owned.
In the story, young George Washington received a hatchet for his birthday. He went out with the hatchet and cut down (or, in some versions, just damaged) one of his father’s cherry trees. When his father asked him what had happened to the tree he admitted that he had done it, saying “I cannot tell a lie,” and then going on to say that he had cut it. There is no evidence that this incident ever actually occurred in real life. Instead, it is a story that was made up about Washington to help make him look like an exemplary person. Americans like to think that Washington was a great person in every way and so this story has stuck around even though the great majority of people today know that it is not true.