Set oven rack to lower third and preheat oven to 475°F.
On rimmed baking sheet, brush potatoes, mushrooms, tomatoes, red pepper and red onion with olive oil and sprinkle with salt and pepper. Bake for 15 minutes, stirring once; let cool slightly and toss with red wine vinegar and garlic.
Meanwhile, line separate rimmed baking sheet with parchment paper. On lightly floured surface, gently stretch and roll dough to prepared baking sheet.
Sprinkle mozzarella over dough and top with vegetables. Bake until crust is browned and top is bubbling and golden, 20-25 minutes.
In bowl, toss together arugula and vinegar; arrange over pizza.