Personally I find your stance far more judgmental than mine; no one needs to 'justify' to someone else why they will or will not commit suicide. It's not even for me to justify or not when someone else does that and I reject your allegation I've done so.
I can't honestly say I know that living in a psychosis (medicated or not) is always better than dying. I defer that judgement to the owner of the body contemplating suicide. Personally no I would not stop the bleeding if asked not to, whether their choice was rational or not. I believe consent and personal choices trump my feelings or trauma from past experiences, even if it turns out the choice of others may be misplaced.
It would be odd indeed if it was OK to stop the dying only if they intentionally performed the action that led to their (imminent) death, but not OK to stop the dying if it was caused by something like a disease.
What is this theoretical individual losing if we help them? What is the society losing if we act to help?
Sadly that is not the reality we live in. The dictator, in this case is New York and various government entities. A government notorious for putting mentally ill in wards where people are "living in filth and dirt, their clothing in rags, in rooms less comfortable and cheerful than the cages in which we put animals in a zoo." [0] Without magic wands, the doctors are not always returning them to neurotypical condition, but rather often some other, perhaps clinically more palatable often drug-induced different mental state. There is often no neurotypical state the wand can be waved to, and often the decision for suicide overlaps between "ill" ad not ill persons particularly when they're subjected to indefinite stays in facilities under conditions of sexual abuse such as historically found in New York mental wards. Hell I might argue it may be cruel to stop someone from committing suicide to avoid being "helped" by New York.
That is, we are dealing with gritty, dirty reality where the mentally ill entity that is the state of New York, itself unqualified in its mental facilities, has a history of sexually and physically abusing people [0, but that's not all] to "protect" them from their own mental illness/suicide etc. Even if the consent argument fails on merits (I disagree), I argue the decision cannot and should not rest on the state in non-criminal concerns of imposing force on the ill (and notwithstanding the dystopic notion of government entities choosing who meets often poorly defined mental diseases).
With the state totally unqualified, and the individual on his own on the street often with family far removed, I defer to his perhaps ill consent. Notwithstanding, of course all help that can be offered should be.
I do not think the alternative society that say maximizes certain utilities at the cost of consent is wrong per se as long as it's possible to freely enter/exit such a society, I just find it incompatible with my values. While I disagree with the notion of stopping someone who has asked his/her respects to be honored in regard to suicide, I don't think it's some moral failing if a private individual makes an in-the-moment reaction to stop them. It's pretty much human instinct to try to preserve innocent life of those around us, so hopefully it hasn't been read that I think you're a bad person or something if you see someone cutting themselves and you stop them.