Heat the coconut oil in a wok or a wide pan over medium-high heat. Add the beets and cook, stirring frequently, for 5 minutes, until beets are starting to soften. Add the seasonings and cook for 2-3 minutes until the fragrance is released. Turn off heat and set aside.
In a separate wok or a large pan, saute the rest of the vegetables for 5-7 minutes, until bright and crisp-tender. Mix in the cooked rice and diced pineapple. Add the lime and the orange juice, and the soy sauce to the pan and cook, stirring frequently, until heated through.
Turn the heat off and carefully stir in the beets. Serve warm.