It has a pretty low success rate, and is likely the sort of thing best reserved for a suicidal gesture rather anything else. According to Geo Stone's Suicide and Attempted Suicide: Methods and Consequences only around 5% of attempters choosing this method succeed. But as he notes cutting, stabbing, etc., statistics conflate suicidal gestures with actual attempts. Having said that, he also notes throat slitting is preferable to any other method of cutting if ending your life is in fact your goal.
I've attached a PDF of Stone's book, the cutting/stabbing method is discussed in Chapter 18. The book itself is worth a read, as much it is now close to 30 years old, so I'm guessing a lot of the drug stuff is now out of date.