Preheat oven to 450 F. Using mandolin, thinly slice potatoes.
Drizzle 9-by-13-inch baking sheet with 1 tablespoon olive oil and spread pizza dough to edges. Shingle potatoes over dough, leaving 1/2-inch border. Season with salt and pepper, to taste, and drizzle with remaining olive oil.
Bake pizza until cooked through and crust is golden, about 25 minutes. Remove and let cool slightly.
Bring small saucepan of salted water to boil. Add green beans and cook until bright green and crisp tender, about 3 minutes. Strain, rinse with cool water and drain well. Transfer to work surface and cut each bean into thirds on bias.
Strain oil from tuna can into small bowl and whisk vinegar into oil. Season with salt and pepper, to taste.
Sprinkle slightly cooled pizza with arugula, tuna, tomatoes, olives, green beans and red onion. Drizzle with vinegar dressing then slice and serve warm.