I'm a firm believer in the ability of physical health to improve one's mental health. The attitude of the body is the attitude of the mind, after all. If you are in a bad mood, you'd be amazed just how much positive impact a workout can have. It can be cardio, Tai Chi, strength training, stretching, anything really. When the body is moved around and feels healthy, that releases chemicals in the brain that help stabilize your emotions.
However, it is important to distinguish between a simple mood swing, and a more serious or chronic mental health issue. Mind-Body techniques can be used to treat many mental health issues, but they are used in a preventative way. For example, mindfulness meditation can help prevent Major Depressive Episodes, but it isn't used as a treatment during these episodes. The same goes for anxiety: if you keep to a mind-body exercise routine while you are feeling good, it's very possible that your anxiety levels will drop, and you won't have as many anxiety attacks. But if you are having an anxiety attack, doing Tai Chi forms is not how you should get through it.
This also applies to non-clinical, chronic emotional states, like grieving or mourning. These are natural processes that require time, loved ones, and often counseling, to properly deal with. If you want to stay as healthy as possible, whether that means losing weight, building muscle, or just being active, it is imperative that you first acknowledge, and seek treatment for, any chronic emotional issues you are experiencing.
Once you are emotionally stable again, then you should develop your mind-body routine and pursue your physical health goals. A peaceful mind can be harnessed to heal and strengthen your body, mind, energy, and spirit. A worried and bothered mind cannot. Weight loss is 50% willpower, and strong willpower comes from a peaceful mind.