Place the beets into a saucepan and fill with just enough water to cover. Bring to a boil, then simmer over medium heat until tender enough to pierce with a fork, about 20 minutes. Drain and rub off peels. Run under cold water until cool enough to handle, then grate using the largest setting. Place in a serving bowl.
Stir the walnuts, prunes and garlic into the beets, then mix in the mayonnaise and season to taste with salt.