"What do you do?" is an idiomatic way of asking "What is your occupation/job?"
And if a plumber is asked to paint a house he might reply "I don't do painting."
The other party might then reply "What do you do?" (Emphasis on the first "do".)
To which a reasonable reply might be "I'm a plumber."
"What is it exactly you do do?" might be the response if a person who had identified himself as a "painter" were asked to paint a house and replied "I don't paint houses." The implication is that the painter is somehow not of the profession his interrogator had assumed, so the interrogator wants more detail as to what exactly the painter does.
In such a case the painter might explain, "I'm an artist, I paint portraits."