In a large pot of boiling salted water, cook pasta until al dente, according to package instructions; drain.
Meanwhile, in a large skillet, heat oil over medium heat. Add half the shrimp; season with salt and pepper. Cook until just opaque throughout, about 3 minutes. Transfer to a large bowl. Repeat with remaining shrimp.
Add garlic and 2 tablespoons water to skillet, and cook until garlic is tender, scraping up any bits from bottom of pan, about 2 minutes. Transfer to bowl with shrimp.
Add pasta, yogurt, lemon juice, mint, and olives; season with salt and pepper. Toss to combine.
Variation: You can replace the shrimp with 12 ounces of thinly sliced boneless, skinless chicken breast.