Cut potatoes into wedges – slice the potato in half lengthwise, then cut each piece in half again to create quarters. Cut each quarter in half or into thirds if the potato is very large.
In a medium mixing bowl, toss potato wedges with olive oil and set aside.
In a small mixing bowl, combine all ingredients for the Cajun spice blend and whisk to combine thoroughly.
Sprinkle 4 tablespoons of the spice blend over the potato wedges and toss to combine.
Place potato wedges on the grill and cook for 10 minutes. Flip potatoes over and cook for an additional 10 minutes (lowering the temperature of the grill if necessary), or until potatoes are cooked through.
Make the dipping sauce by combining mayonnaise with 1 tablespoon of the spice blend and stir to combine.