Preheat the grill to medium-high heat.
In a medium skillet, over low heat, heat 2 tablespoons of the olive oil. When the oil gets hot, add the pine nuts. Season them lightly with salt and cook them, stirring constantly, until they turn golden brown, 2 to 3 minutes. Remove them from the pan to a small bowl. Stir in the minced garlic, salt, to taste, and the mint.
In a large plate, combine the remaining olive oil, the zucchini slices, paprika and light sprinkling of salt. For best results, "dust" the zucchini with the paprika but put it in a little strainer and sprinkle it evenly over the zucchini slices. Toss to coat them with the oil. Season them lightly with salt. Arrange them in a single layer on the hottest part of the grill and cook until they are tender to the touch and charred but not falling apart, 3 to 5 minutes. Use a pair of metal tongs to remove the zucchini from the grill and transfer them to a flat surface. Stack the slices and cut them widthwise into 1/2-inch slices, then make 1 slice down the middle, creating a 1/2-inch dice. Toss them in the bowl with the pine nuts, and then add the lemon juice.
Dip a cloth into some oil and rub over the grill grates. Scatter the clams on the grill in a single layer. Have a pair of tongs and a large platter ready. Littleneck clams take a while to open up, about 10 minutes depending on size, but that's all a part of the fun - the suspense of waiting for them to open. Add a splash of water to help them along and steam. As they open, use the tongs to remove them from the grill and put them on the platter. When they are all opened, scatter the zucchini and pine nuts all around. Try to get the zucchini inside the shells directly on top of the clams and serve immediately.