How does cancer cause death?
That is a subtle question.
The crudest way in which cancer causes death is the tumors, which are actual physical masses (in some cases whole inches) inside a person, damage organs to the extent that they can no longer function. For example, tumors or metastases in the brain make it impossible for someone's brain to work; tumors in their gut actually puncture their intestines. No one can live with that.
Cancer is coming to be seen as a metabolic disease, though this research is less advanced: basically, it can induce metabolic changes in cells and in the body which are incompatible with life.
And the non-cancer way cancer indirectly kills people is chemotherapy. Standard cytotoxic chemo kills dividing cells. Tumor cells tend to divide faster than the body's normal cells so the chemo tends to kill the cancer and leave the person - but often doctors give a patient too much and the patient dies, or the chemo causes some condition (cisplatin - nausea, eribulin - pain) that kills the person instead.