I heard shabbat can be violated if it's to save a life, such as in cases where a doctor needs to heal a patient. But what if it's an licensed Clinical Mental Health Counselor/Art therapist? Let's say there is a Jewish patient that is suicidal and painting is a form of healing their depression. Can an Art Therapist provide therapy where they can paint because it makes them happy?
The Talmud says if someone is experiencing mental illness and a lit candle is causing them severe distress, you can (and should) blow it out on Shabbat. So mental-health concerns clearly qualify.
Next: if right now someone might be suicidal -- save them now and worry about Shabbat later.
This assumes, of course, that this particular form of therapy is needed at this particular moment.
A mental-health professional and a competent rabbi should connect to make sure everyone understands what's actually needed here. But the default is -- save a life first, ask questions later.
I haven't heard of this particular question before about art therapy, but as an example on mental health, many with eating disorders have been told by their rabbis to eat normally on Yom Kippur -- doesn't matter if someone can't fast because they're diabetic, or because they suffer from a mental-health condition that could lead to a horrible spiral in the wrong direction.
Update: This one did actually get explicitly addressed by contemporary sources; if this is what's needed today to prevent life-threatening mental illness, then yes.
Rabbi Yonatan Rosensweig (21st century Israel), נפשי בשאלתי pg. 111 footnote 41 כתיבה או ציור הם מלאכות האסורות מן התורה, ועל כן אין להם היתר בשבת, אלא אם הם מסייעים באופן כלשהו לתהליך הבראתו של חולה שיש בו סכנה (כך, למשל, ישנם מקרים של אנשים בעלי נטיות אובדניות [ולא רק מחשבות אובדניותחולפות], וכגון אלו הסובלים מאנורקסיה שתופעה זו ידועה אצלם, שרק הכתיבה או הציור דוחקים מהם מחשבות אלו, ואצלם הכתיבה או הציור הם בכלל פיקוח נפש)... Writing or drawing are biblically prohibited melachot, and so they are not permitted on Shabbat unless they aid in some way the therapeutic process of a patient who is dangerously ill. (So, for example, there are cases of people with suicidal inclinations [not only passing suicidal thoughts], like those who suffer from anorexia, for whom this phenomenon is known, that only writing or drawing will push aside these thoughts, and for them writing or drawing are including in life-saving activities)…