"Lowered his grip" means that he moved his hand so that he was holding the handle of the ax at the end, away from the ax head. To trace means to draw over a line or shape (such as with a pencil). The soldier held the end of the ax handle and swung it so that the head of the ax followed a semi-circular path. Can you imagine the picture? If someone was threatening your life, and you swung an ax in front of you to keep them away from you, you would be "tracing a deadly semicircle" around you.

If you shift your grip, or lower your grip, you're moving your hand, but grip doesn't mean the hand itself. It means the WAY that your hand is holding a thing. "it fell because I didn't have a good grip."