I've made beet, carrot, and zucchini slaw before. This is the same principle, with shredded raw beets, just with an apple and a little fresh ginger grated in as well.
I used raw golden beets (several small ones), an apple, and a piece of peeled ginger about the size of my thumb. I grated all that together, added a splash of olive oil and apple cider vinegar, and some salt and pepper. That's it, just let it sit for a bit before serving to let the flavors meld.