I assume he's not the editor of a specific department, like business or sports or finance.
If you "pull your punch" when you hit someone, you don't hit them very hard. Two stunt men enacting a fight for the camera will look they are swinging hard, but will pull their punches so it doesn't actually hurt their acting partner.
If you do NOT pull you punches, you hit the person has hard as you are able. It's used as a metaphor, clearly. He does not "go lightly" on the people he wants to attack in the press but hits them with everything he's got.