Which type of cell is responsible for causing apoptosis in cancer cells and virus-infected cells?

The answer is natural killer cells.

Natural killer cells are a type of lymphocytes and they are important for the innate immune system. They recognise stressed cells much faster than other immune cells. Their response is rapid and usually only a few days after a viral infection. They also respond to cancer cell formation. While other immune cells can detect only those harmful cells that have specific markers on the surface of the cell membrane, natural killer cells can even detect those cells that miss markers for apoptosis.