Snap off and discard tough asparagus ends. In a 3- to 4-quart pan over high heat, bring 2 quarts water to a boil. Add asparagus; cook until barely tender when pierced, 3 to 5 minutes. With tongs, lift out asparagus and immerse in ice water. When cool, about 3 minutes, lift out and drain.
Meanwhile, add potatoes to boiling water. Cover and simmer over medium heat until they are just tender when pierced in thickest part, 20 to 30 minutes. Drain potatoes and immerse in ice water. When cool, about 10 minutes, drain and cut into halves. Cut papaya lengthwise into 1/4-inch-thick slices.
Line a platter with salad mix. Arrange asparagus, potatoes, papaya, and olives on greens. Add dressing and salt to taste to individual portions.