Chemotherapy is the only option for oncologists when a cancer has widely spread to different body sites. However, almost all currently available chemotherapeutic drugs will eventually encounter resistance after their initial positive effect, mainly because cancer cells develop genetic alterations, collectively coined herein as mutations, to adapt to the therapy. Some patients may still respond to a second chemo drug, but few cases respond to a third one. Since it takes time for cancer cells to develop new mutations and then select those life-sustaining ones via clonal expansion, “run against time for mutations to emerge” should be a crucial principle for treatment of those currently incurable cancers. Since cancer cells constantly change to adapt to the therapy whereas normal cells are stable, it may be a better strategy to shift our focus from killing cancer cells per se to protecting normal cells from chemotherapeutic toxicity. This new strategy requires the development of new drugs that are nongenotoxic and can quickly, in just hours or days, kill cancer cells without leaving the still-alive cells with time to develop mutations, and that should have their toxicities confined to only one or few organs, so that specific protections can be developed and applied.