Pulse cilantro, mint, jalapeño, sugar, and 3 tablespoons lime juice in a food processor until cilantro is finely chopped. Add half of jícama and pulse until jícama is very coarsely chopped (you want a chunky, crunchy slaw, not a purée). Transfer relish to a bowl.
Pulse remaining jícama in food processor in same manner and add to relish with salt and lime juice to taste. Chill relish well, about 2 hours.
