How does radiation cause cancer and yet is used to cause cancer??

Causing Cancer by radiation is called radiation injuries.
Radiation injuries is damage caused by ionizing radiation emitted by the sun, x-ray machines, and radioactive elements.
Radio and television signals, radar, heat, infrared, ultraviolet, sunlight, starlight, cosmic rays, gamma rays, and x rays all belong to the electromagnetic spectrum and differ only in their relative energy, frequency, and wavelength. These waves all travel at the speed of light, and unlike sound they can all travel through empty space. The frequencies above visible light have enough energy to penetrate and cause damage to living tissue, damage that can be as minor as a sunburn caused by ultraviolet light or as extreme as the incineration of Hiroshima, Japan, during World War II. Lower frequencies do not penetrate, but can cause eye and skin damage, primarily due to the heat they transmit.

Atomic particles can also have enough energy to do damage. They come from radioactive isotopes as they decay to stable elements. Electrons are called beta particles when they radiate. Alpha particles are the nuclei of helium atoms—two protons and two neutrons—without the surrounding electrons. Alpha particles are too large to penetrate a piece of paper unless they are greatly accelerated in electric and magnetic fields. Other subatomic particles are much less common outside of nuclear reactors and particle accelerators.

WHEREAS RADIATION THERAPY IS USED TO CURE (not caused as mentioned in your question) CANCER. – Yes. It is.

Radiation therapy, sometimes called radiotherapy, x-ray therapy radiation treatment, cobalt therapy, electron beam therapy, or irradiation uses high energy, penetrating waves or particles such as x rays, gamma rays, proton rays, or neutron rays to destroy cancer cells or keep them from reproducing.

Radiation therapy is a local treatment. It is painless. The radiation acts only on the part of the body that is exposed to the radiation. This is very different from chemotherapy in which drugs circulate throughout the whole body. There are two main types of radiation therapy. In external radiation therapy a beam of radiation is directed from outside the body at the cancer. In internal radiation therapy, called brachytherapy or implant therapy, where a source of radioactivity is surgically placed inside the body near the cancer.

So Radiation can act both ways viz. it can harm by improper use and it can cure cancer by proper use.-

It has to do with the type of radioisotope used. All radiation is not created equal.To much radiation even the type used to fight cancer can kill you.