In a food processor fitted with the coarse shredding blade, shred horseradish. Change to metal S-shaped blade and whirl horseradish to mince. Add beet; whirl to mince. Add vinegar, sugar, and salt and blend until smooth. Scrape into a bowl, cover, and chill airtight until serving.
*Buy in well-stocked produce markets.
Make ahead: Chill up to 1 week.
Note: Nutritional analysis is per 2 tbsp.