Not sure about the penis, but a fully severed scrotum and testes will cause the subject to bleed to death in under five minutes, unconsciousness usually coming in under two. ("Usually" because different humans have different reactions to blood loss - some go out due to shock in a couple of seconds, others remain compis to the point of heart failure.)

The Human penis is purely hydro in nature, and fed by numerous blood vessels. I would expect any majoer incised wound to be extremely serious.