Some people have died by cutting their wrist or forearm.
When suicide victims choose this method [suicidal incision], they use an easily accessible area and clearly prefer the wrist or the antecubital fossa. (Riviello, 2009. p. 18)
Wrist cutting is rarely lethal.
It is nearly impossible to kill oneself by sanguination secondary to lacerated wrists. The arteries lie deep, protected by muscle, bone, and tendon. in order to get the razor blade deep enough to sever the artery, the suicide must cut through skin, tendons, and muscle. [...] As he becomes unconscious, there is always the chance the blood will coagulate and the bleeding cease before death. (Williams, 2009. p. 40)
It has long been established that overdoses of medication and wrist cutting are low lethality methods. (Rhyne et al. 2010)
This has also been studied in jails, and it is relatively non-lethal, but it can lead to death.
The mortality rates of inmates' attempts by hanging (52 deaths in 602 attempts) was 19 times greater than inmates who cut themselves (1 death in 275 attempts). (McKEE 1988)
Most wrist cutting is not done with the intent of killing oneself.
Interviews with 139 suicidal patients indicate a tendency for suicide attempters using wrist cutting to score low on the Suicidal Intent Scale. (Nielsen et al. 1993)
GEOFFREY R. McKEE (1998) LETHAL VS NONLETHAL SUICIDE ATTEMPTS IN JAIL. Psychological Reports: Volume 82, Issue , pp. 611-614.
Ralph Riviello. Manual of Forensic Emergency Medicine. Jones & Bartlett Learning, 2009
Reuel Williams. The Art of Suicide. AuthorHouse, 2009
Clinton Ernest Rhyne PhD, Donald I. Templer PhD*, Lillian G. Brown PhD, Noel B. Peters PhD. Dimensions of Suicide: Perceptions of Lethality, Time, and Agony. 30 DEC 2010. DOI: 10.1111/j.1943-278X.1995.tb00959.x
Nielsen, Anette S.; Stenager, Elsebeth; Brahe, Unni B. Attempted suicide, suicidal intent, and alcohol. Crisis: The Journal of Crisis Intervention and Suicide Prevention, Vol 14(1), 1993, 32-38.