Preheat a barbecue flatplate or chargrill plate to high, then brush with a little oil.
Meanwhile, whisk ¼ cup (60 g) of the yogurt with the tandoori paste, then brush over the cutlets. Peel and cut the cucumbers into small cubes. Combine in a small bowl with the mint and remaining yogurt.
Cook the cutlets for 3–4 minutes on each side, turning once only. Remove from the heat and leave to rest for 2 minutes. Serve hot, with the minted cucumber yogurt.