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