Preheat oven to 450°. Using a mandoline, very thinly slice the potatoes.
Drizzle a 9-x-13-inch baking sheet with 1 tablespoon of the olive oil and spread the pizza dough to the edges. Shingle the potatoes over the top of the dough leaving a ½-inch border. Season with salt and pepper and drizzle with the remaining 1 tablespoon of olive oil.
Bake the pizza until cooked through and crust is golden, about 25 minutes. Remove and let cool slightly.
Meanwhile, bring a small saucepan of salted water to a boil. Add the green beans and cook, until bright green and crisp tender, about 3 minutes. Strain, rinse with cool water, and drain well. Transfer to a work surface and cut each bean into thirds on a bias.
Strain the oil from the can of tuna into a small bowl and whisk the vinegar into the oil. Season with salt and pepper.
Sprinkle the slightly cooled pizza with the arugula, tuna, tomato, olives, green beans, and red onion. Drizzle with dressing, then slice and serve warm.