Here are some examples of each: It doesn’t matter: “Which cup do you want your coffee in?” “It doesn’t matter. I’ll take any cup you have.” “It doesn’t matter to you which cup you get? Ok, I’ll give you this one.” I don’t mind: “The only cup that is left for your coffee is made of glass. Is that ok?” “That is ok. I don’t mind. I don’t mind that it’s glass.” “Ok, if you don’t mind, then here you go.” I don’t care: This phrase is often less polite than the previous two. “If we don’t hurry, the coffee will get cold.” “I don’t care.” “You might not care if the coffee gets cold, but I will care!”

a matter is a thing of importance. It doesn't matter = it is not important don't mind = Either way will work for me. Don't care = It is not a concern, as mentioned can be meant as indifference through to impolite disinterest