Combine white vinegar, sugar, water, cinnamon, salt, and cloves in a large pot; bring to a boil and stir until sugar has dissolved. Stir in beets and simmer until tender, 15 to 20 minutes.

Meanwhile, inspect six 1-quart jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until beets are ready. Wash new, unused lids and rings in warm soapy water.

Pack sliced beets into hot, sterilized jars, using a slotted spoon, then pour in beet liquid filling to within 1/4 inch of tops. Run a clean knife or thin spatula around insides of jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 30 minutes.

Remove jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Press centers of lids with a finger to ensure lids do not move up or down. Remove rings for storage and store in a cool, dark area.