Roughly peel and then juice the lime. Peel and stone the mangoes.
Transfer the lime juice and mangoes to a food processor or blender. Halve the passionfruit, scoop out the pulp and add all but 1 tablespoon to the blender with the yogurt and ice cubes and process until smooth.
Pour the smoothie into 4 glasses, decorate with the remaining passionfruit pulp and serve immediately.