My homie David the Good recently severed two tendons in his finger with a machette when the hook caught on the brim of his hat in mid swing. The guy is not a novice to machettes or sharp tools and this illustrates perfectly the fact that sharp tools are never safe and that no user is completely accident proof. Occasionally you'll hear someone say that a dangerous tool like a gun or axe is 100% safe as long as it's used properly. That's not a very useful way to look at the problem when humans are always a wild card to some extent. It is the acceptance of danger that leads to the respect we have to embody in order to use these tools as safely as possible. Just as scientists are not vulcans, tool users are not perfect robots and being realistic about ourselves and the often ridiculous beings we are is critical to navigating the use of dangerous tools.
There are a lot of things you can do to yourself with a sharp tool, but few that are fatal or likely to cause serious handicap. Bleeding out is unlikely unless you hit a very few specific spots (Artery on the inside of the thigh being the most likely and not at all infeasible, it happens). The most terrifying injury to me is definitely severing of tendons. Tendons are what attach your bones to muscles so that you can articulate your skeleton and do stuff. They are springy tense things and when cut through, which is easy since they are under tension, they snap. They can be reattached, but there are no guarantees that you will ever function normally again. I knew I guy who cut a tendon in his finger and while stretching during physical therapy the reattached tendon snapped again and couldn't be reattached.
I have tried to take these kinds of lessons and my many injuries and close calls to heart, but it is a constant challenge to me to be aware and step aside look at myself objectively enough to use dangerous tools safely. I think is is as important as anything to simply accept that every time we pick up a sharp tool that we take very real risks. Even a half inch blade is very capable of cutting a tendon in your finger. Next time someone tells you how safe sharp tools are if you just use them right, tell them to STFU. That is exactly the wrong attitude. Best wishes to David for a full and speedy recovery. His unshakable sense of humor can be a model for us all.