Poke each sweet potato a few times and microwave until fork tender, about 10 minutes, rotating about halfway through. Set aside and keep warm.
Combine the chopped carrots, onions, tomatoes, garlic, 2 tablespoons of the vinegar, cumin, 1 teaspoon salt, oregano, cayenne and a few grinds of black pepper in a food processor; pulse until coarsely chopped. Heat the oil in a large nonstick skillet over medium-high heat, add the vegetable mixture and cook, stirring constantly, until dry, 3 to 4 minutes. Add 1/4 cup water and cook, scraping up any brown bits with a wooden spoon, until the water evaporates, about 1 minute. Add the ground beef and cook, stirring and breaking it up into smaller chunks, until browned and cooked through, about 4 minutes. Remove from the heat.
Split the potatoes in half, scoop out some of the warm flesh and add it to the beef mixture; stir to combine. Divide the potato halves among four plates and generously fill each half with the beef-potato mixture. Toss the shredded carrots with the cilantro, the remaining 1 teaspoon vinegar and 1/4 teaspoon salt in a medium bowl. Divide the carrot slaw among the four plates.
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