Preheat the oven to 500 degrees. Place a pizza stone or inverted rimmed baking sheet on the bottom rack.
Mix the garlic and 1/4 cup olive oil in a small bowl. Knead the dough about 6 times on a lightly floured surface. Roll and stretch into a 12-inch round. Place the dough on a pizza peel, or another inverted baking sheet, dusted with cornmeal.
Brush half of the garlic-oil over the dough; season with salt. Scatter the mozzarella and clams over the crust; drizzle with 2 tablespoons of the reserved clam juice and the remaining garlic-oil. Sprinkle with the oregano, parmesan, and salt to taste. Slip the pizza onto the preheated pizza stone or baking sheet (the cornmeal will help it slide off). Bake until the crust is light brown, 13 to 15 minutes.
Just before the pizza is done, drizzle the arugula with olive oil and lemon juice. Slice the pizza; top each piece with arugula and season with red pepper flakes, if desired.