Place the beets, unpeeled, in a pot and completely cover with cold water. Gently boil until they are just tender, about 45-60 minutes, depending on size. Drain and cool beets in cold water to stop the cooking, and then drain again.
Fill a boiling water canner or large pot with water and bring to a boil. While that occurs, peel the beets, and then half and cut into wedges or cut into 1/2” slices and set in bowl. Sterilize 6, 500 mL canning jars in the boiling water for 10 minutes. Remove the jars and boil their snap-top jar lids for 5 minutes.
Pack beets into sterilized canning jars. Place the 2 cups of water, the vinegars, sugar and pickling spice in a pot. Bring to a boil, and boil 3 minutes. Carefully pour mixture over the beets; leaving 1/2-inch headspace and making sure the beets are covered with the liquid.
Wipe rims clean, top with sterilized snap-top lids, and then apply screw band until fingertip-tight. Process sealed jars in boiling water for 30 minutes. Cool at room temperature 24 hours. Check seal. A properly sealed lid curves downward.
Label, date and store the beets in a cool, dark place.