Other forms: psychopathies
Someone who suffers from a mental illness that makes them violent without any sense of remorse or empathy has psychopathy. Although it's a common term in criminal justice, psychopathy isn't an official psychiatric diagnosis.
If someone has psychopathy, they're referred to as a psychopath. As common as these terms are, a psychiatrist or psychologist won't diagnose someone with psychopathy — a patient with these symptoms will likely get a diagnosis of "antisocial personality disorder." A common test measuring psychopathy is used to study prison populations and for sentencing violent criminals. Psychopathy comes from the Greek roots psykhe, "mind," and pathos, "suffering."