In a medium bowl, combine the diced mangoes, red onion, cilantro, and juice of one lime to make the salsa. Set it aside while you prepare the rest of the meal.
In a separate bowl, toss the shredded cabbage and julienned carrot with the remaining lime juice and 1 tablespoon olive oil. Season lightly with a pinch of salt and set the slaw aside.
Pat the shrimp dry, then mix them with the smoked paprika, cayenne pepper, garlic powder, salt, and remaining tablespoon of olive oil until evenly coated.
Heat a large skillet over medium-high heat. Add the seasoned shrimp in a single layer and cook for 2 to 3 minutes per side until they develop a dark crust and turn opaque.
Warm the corn tortillas in a dry skillet or directly over a low flame for about 30 seconds on each side.
Assemble each taco by layering cabbage slaw, several shrimp, and a spoonful of mango salsa inside a warm tortilla.