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Peel root vegetables (remove bitter underlayer if using yuca) and remove any tough cores, then dice. Generously cover with cold water in a large bowl. Cut potatoes into large chunks to expose purple flesh and add to water.
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Heat oil in a Dutch oven or other large heavy pot over medium-high heat until it shimmers. Season pork all over with 1/4 tsp each of salt and pepper, then brown on all sides, 10 to 12 minutes. Transfer with a slotted spoon to a plate.
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Pour off all but 1 Tbsp fat from skillet, then add onion and cook over medium heat, stirring occasionally, until softened, 5 to 7 minutes. Add garlic, chile, paprika, and cumin and cook, stirring constantly, 1 minute
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Add chicken stock, drained root vegetables, and pork and bring to a boil. Simmer briskly over medium-high heat, stirring occasionally, until liquid has thickened and pork and vegetables are tender, 40 to 45 minutes. Stir in lime juice and salt and pepper to taste.
