In a large pot of boiling, salted water, cook the shrimp until pink and opaque, 1 to 2 minutes. Drain and rinse under cold water. Discard the shrimp tails and chop the meat into bite-size chunks. Transfer the shrimp to a bowl. Place the mango in a separate bowl.
In a small bowl, whisk together the olive oil, lime juice, chopped mint, onion, jalapeno and garlic; season to taste with salt and pepper. Pour half the vinaigrette over the shrimp and toss; pour the remaining vinaigrette over the mango and toss.
Spoon a layer of mango into 4 martini glasses. Top with a layer of shrimp, then another layer of mango. Top each serving with a mint sprig.
