Preheat oven to 425 degrees. Loosely wrap beets in parchment-lined foil. Place on a rimmed baking sheet and bake until easily pierced with a knife, about 1 hour. Let cool slightly; remove skins. Slice beets. Set aside.
Season pork generously with salt and pepper. Heat vegetable oil in a large ovenproof skillet over medium-high heat. Sear pork on all sides until golden, about 6 minutes. Transfer skillet to oven and roast until pork registers 150 degrees on an instant-read thermometer, 8 to 10 minutes. Remove from pan and let rest for 10 minutes.
Meanwhile, whisk mustard and vinegar in a bowl. Gradually whisk in 6 tablespoons olive oil until emulsified. Season to taste; set aside.
In a large skillet, heat remaining tablespoon of olive oil over medium heat. Add garlic and cook until fragrant, 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. Add reserved sliced beets and half of vinaigrette, and toss to combine.
Slice pork and drizzle with remaining vinaigrette. Serve with sauteed greens and sliced beets.