Place the cubed pork shoulder, sliced carrots, sweet potato cubes, turnip cubes, diced onion, and minced garlic into the slow cooker insert.
Sprinkle the cumin, oregano, salt, and black pepper over the ingredients, then add the bay leaf.
Pour in the chicken broth and fresh orange juice, and stir gently to distribute the seasonings evenly.
Cover the slow cooker and cook on low for 8 hours until the pork is fork-tender and the root vegetables are soft.
Remove and discard the bay leaf before serving.
Ladle the stew into bowls and top each portion with chopped cilantro and a squeeze of lime.