OK, I have no idea where the minute thing comes from. The fatality rate for stabbings in the UK is 0-8%. Big range, but it only accounts for people who go to hospital; a lot of people who want to dodge epolice or self harm will treat shallow wounds alone. I know someone who was stabbed TWICE, 2 unrelated occasions (London lol). It is really harder than you think to killl through stabbing. There is SI and then, most bleedy spots on your body have a lot of muscle protecting them and it is very hard to cut through this on your own body. A single stab wound is not likely to kill someone especially if it is self inflicted. On abdomen- the most likely cause of death would be infection if your guts are punctured and you don't get medical attention. It would take a lot longer than a minute; more like days and is a nasty nasty way to go.
This is one which has an in hospital mortality outcome of 1.9% from over 530 patients.
Shock would be maybe an ok cause of death, bleeding to death, especially if it is slow, is not great. You don't gently fall asleep as your lifeblood seeps out of you. From people I've spoken to you get symptoms like rapid heart beat, vomiting, ect. I do self harm and I know it's easy to associate the sensation of peace with bleeding, and assume bleeding out would be an extension of that. But vast majority even severe self harm doesn't come close to fatal (your body has an awful lot of blood in it). The endorphins from pain =/= your body slowly shutting down as you bleed out.
People have killed themselves via cutting or stabbing, it's just very hard for someone who isn't acutely psychotic to do successfully and is not a nice way to go. I'm so sorry you feel like this, I know it's awful feeling trapped. I'm sorry if I did come off as a bit of a condescending twat, I had this exact same thought process a few months ago, and in those few months I've managed to wreck my body with a spiralling self-harm habit. Once you get past the psychological barrier of cutting your own flesh open it's very hard to go back. You don't wanna risk either that or infection, those are the likely outcomes.