Men can naturally get rid of their mustache by shaving it. For women, shaving is not the best option because the hair grows back quickly. Repeat shaving is a nuisance and irritates the skin.Sugaring is a better option to remove unwanted facial hair.Similar to waxing, the result can last one to two weeks and the hair that grows back is soft.pply a layer of the sugar mixture to a small area of your mustache. Spread the mixture in the direction of the hair growth, from the bottom of your nose down toward your upper lip. Cover the hairs completely. Place a cotton strip over the sugar mixture. Use downward strokes to help the strip adhere to the mixture.