I imagine someone flaunting a knife in public- whether towards themselves or others is going to cause alarm. I imagine the police's first priority will be to disarm the person- maybe via taser. Then, it's a trip to the psyche ward I imagine- at the very least.
But like others- I'm puzzled really. If it's a serious attempt, why choose such an unreliable method- to begin with? Even if the person manages to cut or stab themselves, medical assistance will be given immediately. If it's a cry for help, ok but I imagine just lingering about on a bridge could have the same effect and scare people less. If it's to deliberately shock and upset people then- I guess the person has their reasons but- it's not likely going to be a targetted 'attack'. It could well be seen by children etc. Personally, I don't support that kind of behaviour.