I'm not a medic, but I was a regular self harmer. To my knowledge cutting is only going to work (aside from if you get sepsis) if you manage to get a major artery and even then they can clot. These are all buried pretty deep in the body.
Wrist wise, when I slit mine I hit tendons. Horrible pain like pins and needles magnified a hundred fold shot up my arm, then my arm went paralysed (temporarily) which hindered doing both. Maybe I hit a nerve too, I don't know.
To be fair it was impulsive, I was a teenager and no resources for research existed like we have today. But it's not a method I'd recommend. I think with cutting its blind luck OR you have medical knowledge of exactly where to cut.