Heat a charcoal grill to medium heat. Place sweet potatoes, and garlic in a large bowl. Crush the saffron over the sweet potatoes and then add the salt, pepper, and olive oil. Toss everything together until the potatoes are well coated.
Place a long piece of foil (about 15 inches) on a flat surface and place the potatoes on one side. Fold the other side over the potatoes and fold the two sides of foil together to make a neat package.
Lay the package next to the charcoal in the bottom of the grill. Cover the grill, leaving the air holes open. Grill the potatoes for about 25-30 minutes, flipping the package halfway through. When the potatoes are pierced easily with a fork they are ready.
Meanwhile, prepare the aioli by combining all the ingredients in a blender. Blend until smooth, adding a bit more water if the mixture is too thick.
Remove potatoes from the grill and serve hot with the avocado aioli for dipping.