I am fairly new here, but my understanding is people cut the dog's hair according to what they like. Some have the "puppy" cut so that they don't have to keep the hair combed and some have the hair long because they think it is pretty.
Some put clothes on the dogs because they like to see their dog's in clothing. We put little shirts on Penny when our house is cold, because she doesn't have fur, but hair like us that won't keep her warm on a cold floor. We have a cute pink coat for going outside in winter also.
So you can give a mutt that is a cross of 5 or 6 different breeds a puppy cut that looks a bit like a schnauzer cut just because that is how you like your dog to look!
And you can dress your mutt in clothes if you like to do that too, or let them run around "naked." if you prefer that.