Mince and mash garlic to a paste with 1¼ 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 in a roasting pan until an instant-read thermometer inserted diagonally 2 inches into center of meat registers 120°F, 25 to 35 minutes for medium-rate.
Transfer to a platter along with any pan juices and cool, loosely covered with foil, 30 minutes to 1 hour. (Internal temperature will rise to about 130°F as it rests.)
MAKE MAYONNAISE: Stir together mayonnaise, paprika, cumin, and ½ tsp pepper. Stir in meat juices and salt to taste.
TO SERVE: Cut meat into thick slices. Serve warm or at room temperature, with smoked-paprika mayonnaise.