Combine the lime juice, maple syrup, soy sauce, and garlic in a small bowl. Whisk in the mustard. Slowly pour in the sesame oil and whisk constantly until the oil is emulsified. (Use immediately or store in an airtight container in the refrigerator up to 2 weeks).
Scrub the potatoes well or peel them, then trim the ends and slice horizontally into 1/4 inch thick rounds. Place in a large bowl, add the marinade, and toss to coat each slice.
Prepare a medium-low fire in the grill. Lift the sweet potatoes out of the marinade with a slotted spoon and grill, turning occasionally and basting with the remaining marinade, until tender when pierced with a fork, 15-20 minutes. Serve hot.