Unfortunately, questions like "What do your parents do?", do crop up more than people think.
My Dad passed away two years ago when I was 16, and I think that the general assumption at such a young age is that your parents are either seperated, or they are still together. People don't seem to consider the possibility that your parent may have died, because it hasn't happened to them, and it is something that young people shouldn't have to experience. It is a kind of innocent ignorance, I find. I even once had a taxi driver that I had met just 10 minutes prior what my parents do, and it is incredibly awkward to respond to if you allow it to be.
I don't tend to cut people off with "He died." I still find those words hard to process myself. Instead, I tend to just talk in the past tense and hope that people get the idea. It doesn't bother me if people ask further questions - I like to talk about my Dad. I don't like people to feel afraid of talking about him as though he is a distant and sorrowful part of my past. He was the most important part of my life.
I also find it extremely insulting that people suggest that parents being seperated is the same as losing a parent. It really, for so many reasons, is not.