First off, most mental illnesses aren't "Cured" they are "treated." I suffer from combat related PTSD myself, and in the past struggled with depression. There have been experiments with using drugs like MDMA to enhance regular therapeutic sessions. The thing is, people in these studies aren't just dropping 3 tabs of acid or getting blitzed off their ass on E like they were going to an EDM festival. There is very solid research showing that abusing drugs actually worsens the severity of depression and PTSD in exchange for a short term escape. The studies using psychedelic drugs as a part of treatment for depression and PTSD utilize extremely low doses of MDMA or psychedelic drugs. The object is not to get high and go on a trip, but to dose the individual juuuuust high enough to loosen their inhibitions and maybe become comfortable enough to talk to a therapist about the things they normally wont discuss. The psychedelics used aren't "curing" anything, they are simply a tiny nudge to help the person open up to their therapist more.
The problem is, that a researcher says "I gave this guy 1/90th of the dose a party goer normally takes and he had an easier time talking to his therapist" and suddenly groups like VICE news and a bunch of other stoner-centric-networks are misquoting the study with headlines like "HEY! OUR FAVORITE DRUGS CURE PTSD AND DEPRESSION!" Its really just an effort to justify their favorite hobby. If you want to drop acid or E and go clubbing, I think its unhealthy, but power to ya. Have fun, drink water, have a designated sober person to supervise and be safe out there. If you want to use it to cure depression and PTSD, you need to see a therapist, not a drug dealer.
Heavy drug use, including psychedelics is devastating for people with PTSD or depression and has been credited as a contributing factor to the high rate of crippling mental issues suffered by returning Vietnam war veterans. I have had several former squad mates develop crippling drug and substance abuse issues in an attempt to "cure" themselves, and it is not pretty. The answer is therapy by a licensed and accredited professional, as nice as it is to envision a magic pill you could swallow to make yourself instantly better, its just not the reality of how mental health works.