Cook fresh or frozen yuca with 1 tablespoon oil in a 6- to 8-quart pot of boiling salted water , uncovered, until tender when pierced with a knife and almost translucent, 8 to 12 minutes for fresh or 10 to 15 for frozen. Transfer with a slotted spoon to several layers of paper towels to drain and let stand 5 minutes. If using frozen yuca, cut pieces into 1/3-inch-thick fries, discarding any fibrous core. Preheat oven to 200°F. Heat about 1 1/2 inches oil in a 4- to 5-quart heavy pot over moderately high heat until it registers 360°F on thermometer. Meanwhile, stir together mayonnaise, lime juice, and minced chipotles (or sauce) in a small bowl. Working in 3 batches, fry yuca, turning, until golden, 5 to 7 minutes per batch, then transfer to paper towels to drain briefly and season with salt. (Return oil to 360°F between batches.) Arrange fries in 1 layer in a shallow baking pan and keep warm in oven while frying remaining batches. Serve with chipotle mayonnaise.