I passed a larger mass during a 30 day juice feast (yes, FEAST not fast) ten years ago. It doesn't mean that it would do that for you, but there are many healing stories regarding juicing and cancer.
Gerson therapy is probably the most high profile treatment for cancer using natural methods.
They employ lots of juice, coffee enemas, castor oil, and home clean up, etc. You could buy Charlotte Gerson's book and it outlines much of what is done in the protocol.
Please see this video on cancer and chemotherapy and it's effectiveness for tumors outside of blood cancer.