Yes, in fact, you should put dishcloths in the dishwasher for cleaning purpose. You can either put them in boiling water for a few minutes for sanitisation. Other sanitisation techniques include throwing them in the washing machine or oven in two three minutes. You should always be attentive to wet dishcloths that are harbouring bacteria, so clean them every time you think it is necessary. You can also use bleaching powder to get rid of the stains on top of the cloth.