A "cure" in this situation means an essentially guaranteed method of treatment. Cancers vary greatly, with some being benign, some being very treatable, and some being extremely deadly (at least with current technology).
My mum beat cancer. She lost parts of her body in the process and chemo changed her physically (her hair and nails never came back the same). It took three years of regular testing to finally be given the "you're officially cancer free" verdict. Three tense years.
All that said she's incredibly lucky not only to have beat it but not to have to live with additional medication due to it. I know somebody who lost a lot more and while is alive now needs a lifetime of medication to "put in" what the partial removed organs no longer produce.
Cancer, as far as I'm aware, goes into remission and isn't cured. Remission is when there isn't any detectable signs of a cancer mass or growth in your body. So imaging doesn't pick up any tumors, your blood work doesn't indicate any hormonal changes, and biopsies come back negative.
A cure would be like say there is no cancer and it won't come back. Remission is more like we have no evidence of cancer and x% of maintain that state for x years.
Fun fact: your body is constantly making cancerous cells, but you have the ability to detect and destroy them before they get out of hand. Keep that immune system strong.
Right now, the main option to "beat" cancer is to poison yourself until enough of the cancerous cells die, along with killing the normal healthy cells. Even then, that only works for certain types of cancer, and that's only if it is treated early enough.
That's very simplistic, there's loads of cancer treatments, what you're describing is a kind of broad brush chemotherapy, but there's lots of more targeted versions, then loads of different pills and potions, immunotherapies, radiotherapies and the good old "cut the thing out" method.
Cancer treatment is the best funded area of medicine and there's loooads of advances going on all the time.