Combine onion and 1/4 cup plus 1 tablespoon lime juice. Cover, and let stand for at least 3 hours, stirring occasionally.
Place spinach in a large bowl. Peel mango. Cut along both sides of the pit to create two portions of mango. Slice each portion lengthwise into 1/8-inch-thick slices. Add to spinach.
Cut remaining mango from pit, and puree in a food processor or a blender with remaining 1/4 cup lime juice (you should have 1/2 cup puree).
Strain onion and add to spinach, reserving juice. Toss shrimp with reserved lime juice, salt, pepper, and cayenne.
Heat oil in a nonstick skillet over medium heat. Add garlic, and cook until soft, about 1 1/2 minutes. Add shrimp mixture, and cook until opaque, about 2 minutes. Add mango puree, toss, and heat through. Add cilantro. Remove from heat, and toss with spinach, onion, and sliced mango. Serve immediately.