Trim beets leaving root and 1 inch of stem; scrub well with vegetable brush. Place beets in a saucepan, and add water to cover. Bring to a boil; cover and cook 35 to 40 minutes or until beets are tender. Drain. Pour cold water over beets; drain. Let cool. Trim off stems and roots, and rub off skins. Cut beets into 1/4-inch slices. Set aside.
Combine sugar and cornstarch in a heavy saucepan; stir in water and vinegar. Cook over medium heat, stirring constantly, until thickened and bubbly.
Add beets to sauce, and cook 15 minutes; stir in butter.