Mix cumin, oregano, smoked paprika, salt, and pepper, together in a small bowl. Rub over all sides of the pork.
Place the pork in the slow cooker, fat side up.
Spread the minced garlic, green chilis, and onions over the top of the pork. Add the juice from the oranges and limes.
Cover and cook on low 10 hours or high 7 hours.
Remove the meat from the crock pot and shred with two forks.
Return the meat to the crock pot and let it simmer on low for 30 minutes.
After simmering the meat, using tongs, transfer the meat to a large rimmed sheet pan. You may need more than one, don’t crowd it. Place it under the broiler for 1-3 minutes. Watch it closely! You want some of the meat to brown up and become crispy, but not all of it.
Serve on tortillas, or alone with rice and beans and garnishes of your choice.