The postulators who are assigned to investigate each candidate for sainthood almost always look at interventions that are medical (with only one recent exception with which I’m familiar), and the consultants (over 60) for the Sacred Congregation of the Causes for Saints are extremely experienced medical doctors, almost all of whom are professors at a medical school or directors of university clinics (the current president is Dr. Rafaello Cortesini, Chief of Surgery at the University of Rome Medical School). They will only examine physical injuries or organic diseases, and will exclude from consideration anything that could be argued to, even possibly, have a psychosomatic cure, which includes all mental illnesses, paralysis, blindness, etc.
They won’t even examine a case until the local diocese has conducted its own investigation, which means that the diocese must collect sworn testimony from the patient and from every doctor, nurse, and technician (whether theists or not) connected with the case. They have to take a signed statement from every witness and family member to ensure that no one invoked the name of anyone for intercession but the candidate for sainthood - that includes Jesus and Mary. Otherwise, the case will be dismissed as evidence for sainthood. Two doctors then have to do a complete physical examination and provide sworn statements that the illness is comletely gone and that there is no chance of a relapse. Until all this is done at the local level, the Vatican won’t even look at the case.
After a review of all that evidence the Sacred Congregation still disqualifies 90 to 95% of the cases because the documentation isn’t sufficient or for other reasons. The Vatican’s medical board, the Consulta Medica, then reviews the cases, and eliminates about half. Then a board of nine theologians reviews the case to see if the case demonstrates clear causality between prayer and the result. If 2/3 of that board votes yes, it goes to a tribunal of bishops and cardinals, who have to vote by a 2/3 majority, then it goes to the Pope, and it is his call.
Very little (any?) “scientific” evidence in academia goes through a process of review that is so rigorous. The cases that are approved are so thoroughly vetted and so beyond what is medically possible that I consider them good evidence for God, and for a God that intervenes supernaturally in some cases, such as the overnight regeneration of skin from third-degree burns over the entire body.
An example of cures of mental illness would include those attributed to the intervention of the Venerable Matt Talbot, a blue-collar Dublin dockworker whose miraculous intervention against alcoholism and other drug addictions through fasting and ascetism resulted in over a thousand sworn testimonies that were sent in support of his sainthood when the Blessed Pope John Paul supported his candidacy for sainthood. All were disallowed by the Congregation, because only the healing of a physical ailment could be verified using scientific principles.
That doesn’t mean the thousands - probably millions - of cures of mental illnesses aren’t miracles. Talbot himself, although not yet a saint, has nevertheless been honored by being declared the patron saint of alcoholism by the Vatican. He is known throughout the world, especially in Ireland, the U.S., and Poland, and you can find statues of him everywhere.
*“Three things I cannot escape: the eye of God, the voice of conscience, the stroke of death. In company, guard your tongue. In your family, guard your temper. When alone guard your thoughts.”
- The Venerable Matthew Talbot*
You can learn more about him here:
catholicireland.net/pages/index.php?nd=68&art=513