That movie is so violent it looks like a parody of violent movies rather than an actual movie that is meant to be taken seriously as a violent movie. What's different between the US version and the Japanese version? Well the US theatrical version cut a lot of scenes and converted others to black&white footage (red blood must be more offensive than dark gray blood) to keep it rated R (otherwise it would have been NC-17, for violence, which is unusual as NC-17 is usually reserved for porno films, so yeah it's VERY violent). But there was never a "directors cut" or "unrated version" released on DVD in the US that would have shown the film uncensored/uncut like a number of other movies have done. Instead that's what the Japanese DVD release has. It is fully unedited. A bad guy gets his head chopped off with samurai sword, which then causes a fountain of blood gushing like 10 feet high (something like you'd expect to see in an anime movie). Lots of other people lose lots of limbs, each of which is shown having blood spraying out of the body at the place where the limb was missing, like water out of a garden hose, with the nozzle set to an almost misty spray. Like 100 guys try to take out the heroine of this show, only to be severely dismembered by her uber ninja skillz with her katana. One guy gets split right down the middle, from the top of the head, straight down, and he falls in half, his left side to the left, his right side to the right.
So if you are up for watching an ultra, beyond belief, bloody, violent, sword fight movie, get a copy of the Japanese version of Kill Bill. If you can't find an actual DVD of it, download the torrent (which I won't link to here, because AF doesn't condone piracy).
By the way, here's an interesting bit of trivia:
They used so much fake blood in this movie that they ran out before the end of filming, and had to substitute water for a couple of the blood spray scenes (resulting in clear blood gushing out of the wounds in one or two scenes, and pink diluted blood in another scene or two). This isn't noticeable in the US version where the entire big sword fight scene is shown in black&white, but is easily seen in the Japanese version which has that entire fight scene in color.