For the garlic sauce: Puree the garlic in a food processor. Add the mayonnaise, jalapeno, mint, cilantro, salt, lime juice and vinegar; process until smooth.
For the plantains: Fill a large heavy-bottomed pot with 2 inches of oil and heat to 350 degrees F.
Combine the salt, smoked paprika, cumin, cayenne, and black pepper to taste in a small bowl; mix to blend.
Trim the ends of the plantains with a paring knife. Score the skins lengthwise in a few spots, then peel. Slice the plantains lengthwise into thin planks, about 1/8-inch thick.
Fry in batches until golden brown, 5 to 8 minutes. Drain on a paper towel-lined plate, then toss with the spice mixture.
Serve the chips with the dipping sauce.