Put chicken breast halves between pieces of plastic wrap and pound with a meat mallet or the back of a small, heavy saucepan until 1/4 in. thick. Whisk lemon zest, olive oil, 1/2 tsp. salt, 1/2 tsp. pepper, the smoked paprika, and cumin together in a small bowl. Put chicken breasts in a large, wide bowl and add marinade, rubbing all over chicken to coat. Cover and chill at least 3 hours and up to overnight. Allow chicken to come to room temperature before grilling. Meanwhile, rinse onion and dry it with paper towels.
Prepare a gas or charcoal grill for medium heat (you can hold your hand 1 to 2 in. above cooking grate only 4 to 5 seconds). Lay chicken on well-oiled grate and cook, turning once, until cooked through, 6 to 8 minutes. Transfer chicken to a plate or cutting board, tent with foil, and let rest 5 minutes.
Meanwhile, whisk yogurt, harissa, 1 tbsp. mint, remaining 1/4 tsp. salt and 1/4 tsp. pepper, and the lemon juice together in a small bowl. Slice chicken on the diagonal across the grain into 1/4-in.-thick strips.
In a large bowl, toss together greens, carrot, bell pepper, onion, and olives with 1/2 cup dressing until just coated.
Divide salad among 4 plates and top with chicken. Drizzle remaining dressing over salads, dividing evenly, and garnish with remaining mint.
Note: Nutritional analysis is per serving.