Preheat oven to 500°F with rack in middle.
Mince and mash garlic to a paste, along with 1-1/4 tsp salt. Transfer to a small bowl and stir in paprika, cumin, oil, and 1 tsp pepper.
Pat tenderloin dry, then rub garlic mixture all over it. Roast meat in a roasting pan until an instant-read thermometer inserted diagonally 2 inches into center of meat registers 120°F, [about 25 to 35 minutes] for medium-rare doneness.
Transfer to a platter along with any pan juices and cool, loosely covered with foil, 30 minutes to 1 hour. (Internal temperature will rise another 10 degrees to about 130°F as it rests.)
Stir together mayonnaise, paprika, cumin, and 1/2 tsp pepper. Stir in meat juices and salt to taste.
Cut meat into thick slices. Serve warm or at room temperature, with smoked-paprika mayonnaise.