Using food grinder with coarse blade, grind beets, apples, and onions.
In large kettle or Dutch oven combine ground mixture, sugar, vinegar, water, cinnamon, and salt.
Bring to boiling.
Cover; simmer for 20 minutes, stirring often.
Ladle hot relish into hot, clean half-pint jars; leave 1/2-inch headspace.
Process in boiling water bath for 15 minutes. (Start timing when water returns to boiling.)