In a bowl, combine the grated beets, sugar, salt, chives, lemon juice, mandarin juice, black pepper, coriander, and lemon and mandarin zests and mix well. Set aside.
Pat the salmon dry. Lay a large piece of plastic wrap on a work surface and spread half of the beet mixture on an area of the plastic wrap about the size of the salmon. Lay the salmon skin-side down on top of the mixture and cover it completely with the remaining mixture, gently pressing it to the flesh. Wrap the salmon tightly with the plastic wrap and place in a baking dish or set on a rimmed sheet pan to cure. Refrigerate for 24-36 hours, turning the salmon halfway through.
Unwrap the salmon and scrap off the beet mixture. Quickly rinse the salmon under cold water to remove the remaining cure.
Using a sharp knife, thinly slice the salmon on the diagonal, leaving the skin behind. Serve chilled with your favorite sides or toppings. I love to serve it on a bagel with cream cheese or alongside jammy eggs for breakfast, or with cucumber and tzatziki for a mini meal.