An evil-doer is someone who does cruel, immoral, or criminal things — a person who chooses to cause harm. The word feels a little old, and a little like a sermon or a storybook: you meet it in the Bible, in moral talk, in fantasy, and in headlines that want a sharp moral punch. In ordinary conversation people more often say criminal, wrongdoer, or simply a bad person. “Doer” here is just “a person who does that thing,” the same pattern as in wrongdoer. Calling someone an evil-doer is a strong judgement; it is not a light or joking word unless you are clearly playing with the old-fashioned tone.