Score mango flesh in a cross-hatch pattern about an inch apart, being careful not to cut through skin. Grill, flesh side down until grill marks appear and flesh turns golden brown, about 2 to 4 minutes. Transfer mango, flesh side up, to a platter until cool enough to handle. Take a mango slice and push from skin side to turn inside out. With a sharp knife, cut grilled mango flesh away from the skin; discard skin.