Bring a medium saucepan of water to a boil. Peel the sweet potato and slice it into 1/8-inch slices. Drop the slices into the boiling water and boil until just tender, but not falling apart, about 5 to 7 minutes. Drain the sweet potatoes, then set aside.
Heat the grill to medium-high.
Grill the sausage slice until charred and cooked through, about 3 minutes on each side. Remove from grill and set aside.
Clean the grill grate and brush with oil. Stretch the pizza dough into a rough circle, about 14 inches in diameter. Lower the grill to medium heat, then set the dough on the grate. Close the lid and grill for 5 to 7 minutes, or until the bottom is toasted and golden.
Brush the top of the pizza crust with half of the olive oil and flip over. Brush again with the remaining oil. Top with the sweet potato slices, the cooked sausage pieces and the mozzarella slices. Close the grill and cook for 7 to 8 minutes, or until the cheese is melted and the bottom of the crust is golden and crispy. Remove from the grill and sprinkle with salt, pepper and thyme.