Does China allow movies like the Saw franchise? If not, all hail the Han!

Not quite, but they do allow for A LOT of really gruesome gore, so long as it's done to promote nationalism. A perfect example is Operation Red Sea.

You thought the first 15 minutes of Saving Private Ryan was gory? Imagine two whole hours with that level of gore, but WORSE. They spare no expense to show you what happens to suicide bombers, and what happens to civilian victims caught in crossfires/explosions.

It's one of -- if not the most goriest movie I've ever seen. But it was a-okay by Chinese standards because it made the Chinese special forces look like top-notch, Rambo-class badasses.