Add the pork cubes, sweet potato cubes, diced onion, and minced garlic to the slow cooker.
Stir in the chopped chipotle peppers, diced tomatoes with their juice, chicken broth, cumin, smoked paprika, salt, and black pepper.
Cover and cook on low for 8 hours or on high for 4 hours, until the pork is very tender.
Taste and adjust salt or pepper if needed before serving.
Ladle into bowls and top with chopped cilantro and a squeeze of lime.