"But what kind of work do you do?"
would be translated into:
a1) Che tipo di lavoro fai?
a2) Che lavoro fai?
Please take note that int THIS CONTEXT the word 'razza' refers to animal species or actually a particular breed among a species, like in /che razza di cane e` il tuo?/
If you ask:
/che razza di cane e` il tuo?/
it would be a simple and emotionally neutral question.
When you ask:
/che razza di lavoro fai?/ the word /razza/ has a derogatory meaning so the full meaning would be:
a) What kind of work do you do
b) I think your work is ugly, or too heavy, or humiliating, or maybe I even think that you are doing something related to crime.
Note that the (b) meaning which will be there, has many possible sub-meanings, some of them showing empathy with the person and
while others would be in complete personal disagreement.