How do electrons destroy DNA bonds in radiation?
I think you have a fundamental misunderstanding of the chemical reactions involved in radiation therapy. Neither photon based or proton based therapies "create electrons", but they do cause ionization by adding enough energy to existing electrons around atoms so that the electron is ejected from the atom, creating an ion or free radical, which can then undergo chemical reaction.

Photons, typically gamma rays, X-rays, and high energy UV, typically interact with water molecules and produce free radicals, including the dangerous hydroxyl radical. The hydroxyl radical can interact with proteins and DNA and damage those molecules, but has a very short half-life. Molecular oxygen can help increase the damage by reacting with the hydroxyl radical to produce Reactive Oxygen Species, ROS, which can also damage DNA or protein. However, many tumors have low oxygen concentration that reduces the effectiveness of photon based radiation therapy.

To overcome this, many patients receive proton based radiation therapy. Protons are much heavier than photons (I guess infinitely heavier than a photon, since photons have no mass) and therefore scatter to a much smaller extent. They just sort of plow through tissue and knock electrons out of orbitals as they collide with molecules such as DNA or protein. They don't rely so much on free radical generation or ROS, so low oxygen levels don't reduce their effectiveness.

The goal is damage the DNA to induce double strand breaks which are hard to repair in fast growing cancer cells. Because they grow so quickly, they are already stressed and their DNA repair machinery is less effective than in healthy cells. If their DNA can be sufficiently damaged, the cell will die.

For more information about these processes, please see these wikipedia articles on Radiation Therapy, Radiolysis, Linear Energy Transfer, and Free Radical Damage to DNA.