When James talks about saving "a sinner from death," he means more than just physical death. He is referring to eternal death, which is the punishment for those who turn away from the truth of the good news of Jesus Christ (see 1:12, 15; compare Hebrews 6:4–8).
James teaches that if someone has wandered from the truth, other believers should try to bring that person back to the right path. If the person who has sinned listens and turns back to God (repents), then eternal punishment will be avoided (see also Galatians 6:1; Jude 1:22–24).