"Chipped Apart" describes a girl who is hurting badly on the inside while everyone around her accepts that she's fine. The speaker sets up a painful contradiction: she tells people she's okay, they believe her, and yet she wishes they wouldn't. What she really wants is for someone to question her answer and ask what's wrong.
The feeling moves from sadness to frustration, then to blame. The speaker wonders why no one looks deeper, and eventually suggests that people don't want to admit they failed her. The line about them watching as she "slowly crumbled down" is the sharpest accusation, because it makes their silence an active choice rather than an accident.
The short, broken lines and sudden line breaks, such as "her" standing alone, mirror the idea of something breaking apart piece by piece. The mood is lonely, resentful, and quietly desperate. The final line, "and they did nothing," leaves the reader with a bleak sense of how easily suffering can go unnoticed.