Preheat oven to 400 degrees. Loosely wrap beets in a 12-by-20-inch piece of foil. Place on a rimmed baking sheet and bake until easily pierced with a knife, 35 to 45 minutes. When cool to touch, grab beets with a paper towel and slip off skins. Reserve one beet; halve and slice remaining beets. Set aside.
Season pork generously with salt and pepper. Place on a rimmed baking sheet and roast until pork registers 150 degrees on an instant-read thermometer, 14 to 16 minutes.
Meanwhile, in a food processor, combine the reserved beet and 1 tablespoon oil; process until smooth. Strain through a fine-mesh sieve (or strainer) lined with cheesecloth into a small bowl to yield 4 teaspoons juice; discard solids. Add mustard, 2 teaspoons vinegar, and 2 tablespoons oil; whisk to combine. Set aside.
In a large skillet, heat remaining tablespoon of oil over medium. Add garlic and cook until fragrant and golden, about 1 minute. Add beet greens, season with salt and pepper, and cook, stirring occasionally, until wilted and tender, 2 to 4 minutes. Remove greens from heat and discard garlic. Add reserved beets and remaining tablespoon of vinegar, and toss to combine.
To serve, top sauteed greens with toasted pine nuts. Drizzle a little of the beet vinaigrette on the plate and top with sliced pork.