Cut mango into 4-in. cubes and select about 20 of the nicest ones. Cut jicama into thin slices about the same width as the mango pieces.
Put lime juice, salt, and jicama in a bowl and toss to coat. Lift out jicama and set aside. Add mango and chopped cilantro to bowl along with salt to taste; toss to coat.
Arrange a cilantro leaf on a slice of jicama, top with a mango chunk, and skewer together from the top with a toothpick. Sprinkle with cayenne to taste. Repeat to make remaining stacks.
MAKE AHEAD: Chilled airtight, up to 2 hours.