Pour 1/3 cup of beet juice into a measuring cup and reserve. Put the beets and their remaining liquid in a saucepan and place over medium heat. Bring the beets to a simmer; drain and transfer to a bowl.
Zest enough of the orange to make 1 teaspoon. Squeeze 5 tablespoons of orange juice. Add the orange juice and zest to the reserved beet juice.
In the same saucepan used to cook the beets, combine the cornstarch, vinegar, brown sugar, and the beet and orange juice mixture; whisk to blend.
Bring the mixture to a boil over medium heat.
Add the beets and butter to the saucepan and heat for 2 to 3 minutes or until hot.