Cut the turkey into bite-size pieces and place them in a bowl. Add the garlic, honey, lime zest and juice, mint and yoghurt. Toss well to coat evenly. Place the turkey in the refrigerator to marinate for 1-2 hours, or preferably overnight, to allow the flavours to develop.
Heat a barbecue or grill to a medium heat. Toss the mushrooms in the turkey mixture to coat them with the marinade. Thread the turkey pieces and mushrooms alternately onto skewers, then sprinkle with salt and pepper to taste.
Grill for 8-10 minutes, turning the skewers occasionally, until the turkey is golden brown and the juices run clear when the pieces are pierced with a knife. Serve with wedges of lime.