I remember there being an episode of the 1982 cartoon version of The Little Rascals (I was nine years old when I first saw it in 1983) in which Spanky was learning how to perform magic and puts on a makeshift magic show performing as the Great Spankini, and one of the acts was he trying to saw a man in half (it was really Buckwheat on one end, and Porky on the other, and both boys were "little kids" as opposed to Spanky, Darla and Alfalfa.
In comic books, there was a Looney Tunes story (from the Whitman Comics series) in which a character was performing the trick of sawing Petunia Pig in half - and she felt minor pain and/or her dress was ruined.
Thankfully, I don't recall that trick being performed on the primetime special It's Magic, Charlie Brown. Snoopy would fail at all of his magic tricks except for the disappearing act - in which he successfully made his owner, Charlie Brown, invisible.
I agree, uncertainty on whether someone could get hurt is the reason why we don't see the "saw a man in half" trick being performed now. Kids these days - and maybe even millennials when they were kids - seem to get creeped out when they see such trick being performed. But I'd like to ask, did The Amazing Mumford ever attempt that trick on Sesame Street?