Trim any excess thick fat from the pork shoulder and cut into 2-inch chunks.
In a small bowl, mix the cumin, dried oregano, sea salt, and black pepper.
Rub the spice mixture over the pork chunks and place them in a slow cooker.
Add the minced garlic cloves, orange juice, and lime juice to the slow cooker.
Cover and cook on low for 7-8 hours or on high for 4-5 hours until the meat is fork-tender.
Remove the pork from the slow cooker and shred with two forks.
Optional: For crispy edges, place the shredded pork in a non-stick skillet over medium-high heat for 3-5 minutes until browned.
Warm the corn tortillas in a dry pan until pliable and slightly toasted.
Divide the shredded pork between the tortillas.
Top with finely diced red onion, chopped cilantro, and thinly sliced radishes before serving.