Grate the cucumber onto a plate using a coarse grater. Place the grated cucumber in the centre of a clean tea towel. Gather up the edges to enclose the grated cucumber and squeeze over a small bowl, to extract as much liquid as possible. Discard the juices and place the squeezed cucumber in the small bowl.
Add the yoghurt, garlic, lemon juice, mint, dill and salt. Stir until evenly combined. Serve at once or cover and chill until ready to serve.