Sugar is a pretty broad term (fructose, galactose, lactose, sucrose, glucose are all different types of sugar). In a really over simplified way almost everything you eat gets converted to glucose at some point. That glucose is then used to create ATP via cellular respiration (the Krebs cycle) to power your cells. There is "sugar" in everything you eat. There are stores of glycogen, a stored version of glucose, in the muscles of the animals you eat. So yes, there is "sugar" in steak, chicken, pork etc.
So cutting down on sugar likely wouldn't have an effect. Once again in an over simplified way all your cells are powered by sugar, cancerous cells aren't unique in this way. I'm not a biologist though so I could be wrong.
