Add the pork chunks to the slow cooker.
Scatter the minced chipotle peppers, sliced onion, and minced garlic over the pork.
Pour in the chicken broth. Sprinkle the cumin, oregano, salt, and black pepper on top.
Cover and cook on low for 8 hours.
Shred the pork directly in the slow cooker using two forks and stir it into the juices.
Warm the corn tortillas in a dry skillet or microwave just before serving.
Spoon the carnitas into the tortillas and top with cilantro and a squeeze of lime.