There are two sets of death that describe Little Tree's coming of age. The first deaths are the deaths of his own grandparents, which symbolize the death of human beings. His caretakers are not immortal, and now that they are gone, Little Tree must take care of himself until he cannot. This frames the story of life from beginning to end, because he must see his own life through to its conclusion, hoping along the way to help others the way his grandparents helped him. This also symbolizes the inevitable death of his culture as the indoctrination of schools suggested to him in childhood.
Then there are the deaths of the dogs as he sojourns. This symbol is also a set of opposites, because the dogs are named Red and Blue, and just as the human deaths symbolize something uniquely human, the dogs symbolize nature. Namely, the dogs symbolize the connection between Little Tree and nature through his own animal nature. He is Cherokee in his point of view, so he doesn't draw any hard lines between his own nature and the nature of his pets, whom he considers family. The dual death of human and animal point to the dual nature of human nature.
The other half of human nature is not like the dogs which die. Though the human body dies, the grandparents teach Little Tree that they will always be spiritual companions to him in his mortal journey, and that death is only a transport to a new consciousness which does not die. This spiritual idea is deeply ingrained in him (and in most of the world's tribal populations, in fact), and with that third set of pairs, the portrait is complete. Little Tree has passed his grandparents in time, and he has outlived his dogs, two sets of death, but the immortal, invincible spirit that survives death is the invisible third pair that well help Little Tree in his life, like the wind.