Process all ingredients except chicken in blender until smooth paste forms, 10 to 20 seconds. Using fingers or handle of wooden spoon, carefully loosen skin over thighs and breast and remove any excess fat.
Using gloves, rub half of paste beneath skin of chicken. Spread entire exterior surface of chicken with remaining paste. Tuck wing tips underneath chicken. Place chicken in gallon-size zipper-lock bag and refrigerate at least 8 hours and up to 24 hours.
Adjust oven rack to lowest position and heat oven to 325 degrees F. Place a 12-ounce can of beer on baking dish with high sides. Slide chicken onto beer can so chicken stands upright and breast is perpendicular to bottom of pan.
Roast until skin just begins to turn golden and instant-read thermometer inserted into thickest part of breast registers 140 degrees, 45 to 55 minutes. Carefully remove chicken and pan from oven and increase oven temperature to 500 degrees F.
When oven is heated to 500 degrees F, place 1 cup water in bottom of pan and return pan to oven. Roast until entire skin is browned and crisp and instant-read thermometer registers 160 degrees inserted in thickest part of breast and 175 degrees in thickest part of thigh, about 20 minutes (replenish water as necessary to keep pan from smoking), rotating bird 180 degrees halfway through cooking. If the top of the chicken is becoming too dark during roasting, place a 7-inch-square piece of foil over the neck and wingtips.
Carefully remove chicken from oven and let rest, still on the can of beer, 20 minutes. While the chicken is resting, mix all the spicy mayo ingredients. Afterwards using a kitchen towel, carefully lift chicken off beer can and onto platter or cutting board. Carve chicken and serve with spicy mayo.