"Why does he say that?"
Translation:Warum sagt er das?
To start with, your proposal lacks an object that is necessary for a meaningful phrase. Thus you better say:
- Warum sagt er das so?
- Warum sagt er es so?
However, both phrases mean something like Why does he say it this way [that way/ like so/ like that/ in this manner]? That's not exactly what the original phrase means.