Clinically, I've had great results with acupuncture in the treatment of depression & anxiety (except in one case where the patient's anxiety made receiving acupuncture impossible. To that, I can only say that not every modality is right for every person).
If a patient is currently taking medication, I like for them to at least initially stay on their medication. Later, as they improve, they can talk with their physician about slowly coming off of their anti-depressant or anti-anxiety medication. (Please note: some of these medications have severe withdrawal symptoms that should not be taken lightly. Always speak to your MD first!)
It's also not a bad idea to continue seeing a psychotherapist. The patients who have the best results are those who simultaneously work on the physical, mental and emotional aspects of the disease with acupuncture and the social, behavioral, and psychological aspects with a professional in that field.
Here's an article from Scientific American from back in 2014: