Cancer related surgeries have absolutely no way to remove genes. For example, BRC1 is a gene, inherited from a parent, which has been linked to breast cancer. You start out as one cell which divides again and again making copies of itself and eventually become a baby etc. Whatever genes were present at conception are in all of your cells. A surgery doesn't remove these genes, just the tumor.
As for death, in order for natural selection to take place and thus remove a deleterious gene from the population, those who have the gene have to be affected by it BEFORE they have kids. Say for example a baby gets a mutation that causes a new disease no one has ever heard of. They die when they're 5 years old. After they die, there are no more copies of this bad gene in the population. With breast cancer most women are in their 50's when diagnosed. This means they have already had kids and passed on their genes. To top it off all if their kids inherit a gene such as BRC1 from their mom, they they pass it on to their kids before they develop cancer and die (if they even get cancer).
There is a chance of breast cancer genes to be inherited from parents to their kids So as long as the cancer carriers still reproduce, the cancer gene will always be present in the population
