Can you use diet as a substitute for chemotherapy?  No.  No serious scientist or doctor will tell you you can significantly affect your cancer prognosis.  Many studies have searched for a connection but no strong evidence has ever been found.  The macrobiotic food evangelists sometimes tell people their diet can cause remission of cancer but there is no science to back them up.  No experimental data and no credible hypotheses about how it would work.

What about diet as a way to prevent cancer?  Or at least to reduce the risk of development and growth of malignant tumors?  This idea is more scientifically plausible, but there is no hard evidence   Some feel certain phytochemicals (from plants) can have antiangiogentic effects.  Of course your body manufactures angiogenesis inhibitors on its own so we might ask if phytochemicals are needed.  Nobody knows the answer to this question.

Nutrition during cancer treatment

Now there are reasons to pay special attention to what you eat during treatment.  A change in diet may help you weather side effects better.  The National Cancer Institute and the Cleveland Clinic have good webpages on this.