It's not a 'why' question but a 'when' question. You see, predicting is a very important part of listening. In your native language you just never notice how you always predict words and sometimes the whole phrases. there are plenty of studies on this subject. To be able to hear 'what ARE you doing' you have to learn present continuous and be able to use it accurately. Then it will be just a matter of time when you start to hear the correct phrases. Take children, for example. When they hear a difficult word from adults or grammar structures they've never heard before they can hear them wrong and repeat wrong. And then adults correct their mistakes and ask to repeat the word correctly so that next time they hear it they'll recognise it.

Why I usually mistaken "are" with " do" in the American series(*?)

Why I usually mistaken "are" with " do" in the American series. 
such as For example, "What are you doing?" actually(**) sounds like, "What do you doing?"
and, "What are you talking about?" sounds like, "What do you talking about?"
especially when they speak very fast.

*If you meant speech, as in how Americans talk, this should be, "American speech". If you are talking about a TV series, you should say, "American TV series", because if you just say, "American series" it sounds a bit strange and could mean several things. Someone might think you are talking about a series of books, for example.

**Normally you use "actually" to correct a misconception. What follows "actually" should be a fact, not an opinion. If you wanted to use actually here, you could put "to me," before it. Instead it would read, "'What are you doing?' to me, actually sounds like, 'What do you doing?'". You could also just get rid of actually, like you did in the second example you gave.

You're exactly right, Eva. In fact, it's quite typical to omit the auxiliary verb entirely in this type of question. That is say, questions in the second person are spoken without are, do, or have. You'll also hear the blended pronunciation "watcha" in this context. Note that the main verb will be in the present participle, the base form or the past participle, as appropriate.