Trivia: Bafflingly, despite having little sex or profanity, and only minor cartoonish violence, the film was slapped with an NC-17 rating when it was first submitted to the MPAA. Everyone involved with the film was shocked. Turns out, a single 1-second shot of a little black, blood-like goo splashing onto a wall following a decapitation was the reason the MPAA gave the film an NC-17. Once it was cut, the film was reduced to an R.
Suggested correction: While it's true that it initially got a NC-17 rating, it wasn't because of a 1-second shot of goo. It was mainly for the decapitation scene and ostensible gore. Director Sam Raimi trimmed down the decapitation scene, but refused studio pressure to trim the movie down to a PG-13 rating, so most of the people involved in the actual making of the film weren't expecting a PG-13 rating.
The one-second shot was from the decapitation scene you mentioned. It's the shot the bloody goo splashing on the wall after he slices the hag's head off. As for the second point, upon looking around, I'm finding conflicting reports. I've only really seen one or two sites saying Raimi "refused" to trim the movie down, and many more that imply he tried to appease them for a PG-13 and had no reason to believe it would be rated R/NC-17 due to how cartoonish the film is (several of these sites also cite a book as evidence, but I can't find the book online). But given there are conflicting reports, I'll edit out the last bit.