With a knife cut slits into the pork and stuff half of the garlic into the slits. Place the pork into a large sealable container.
Combine the remaining garlic, jerk seasoning, and salt and rub over the pork.
Mix the lime and orange juice and pour over the pork. Cover and marinate the pork for 5 hours or overnight.
Spray a slow cooker with cooking spray and place the pork and marinating juice into the bottom of the slow cooker. Cook on LOW for 8-9 hours.
Once the pork is cooked and tender, remove the pork and shred it. Place the shredded pork back into the slow cooker with the juices. Cook for an additional 15 minutes.
To make the Caribbean salsa:
Mix the diced mangos, avocado, and red onion. Add cilantro and lime juice and salt and pepper to taste. Serve over the pork.