Mix white vinegar, sugar, water, cinnamon, salt, and cloves together in a large pot; bring mixture to a boil and stir until sugar has dissolved. Stir in beets and simmer until tender, 15 to 20 minutes.
Sterilize the jars, lids, and rings in boiling water for at least 5 minutes. Using a slotted spoon, pack the sliced beets into the hot, sterilized jars, and pour in beet liquid to fill the jars to within 1/4 inch of the top. Run a sterilized knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids, and screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil over high heat, then carefully lower the jars into the pot using a holder. Leave a 2 inch space between the jars. Pour in more boiling water if necessary until the water level is at least 1 inch above the tops of the jars. Bring the water to a full boil, cover the pot, and process for 30 minutes. Add more time if you are at high altitude.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.