Preheat a grill to medium (about 350 degrees F) on one side. Pour the beer into a turkey sitter (a ceramic stand that holds liquid). Or open the beer can, pour out a few tablespoons and place in a beer-can turkey stand.
Combine the mustard powder, garlic powder, dried onion, paprika, granulated garlic, cumin, and salt and pepper to taste in a small bowl.
Remove the neck, giblets and any excess fat from the turkey; discard. Rinse the turkey under cold water and pat dry with paper towels. Rub the cavity with 2 to 3 teaspoons of the spice mixture. Brush the outside of the turkey with the canola oil and place drumstick-end down on the sitter or stand. Rub the remaining spice mixture all over the turkey.
Place the turkey (on the sitter or stand) on the cooler side of the grill. Cover and cook until the juices run clear and a thermometer inserted into the thickest part of the thigh registers 185 degrees F and 170 degrees F in the breast, 2 to 3 hours. Carefully remove the turkey from the grill, remove from the sitter or stand, and discard the beer. Transfer the turkey to a cutting board and let rest at least 20 minutes before carving.