I don't think this is as common of a method due to it's pain and reliability. In other words, it is really painful to cut yourself and even scarier knowing that the blade will cause grievous harm. Also, depending on where the blade cuts, you might survive in a lot of pain and disfigurement. I'm sure there are ways or similar methods carried out with blades, knives, and swords but just uncommon (the one that comes to mind is a suicide back in the early 2000's of a guy who made a homemade guillotine).
Another thing is that swords aren't as easy to come by in certain parts of the world and most of them are used for antiques, collections, or sports/fencing in general.