In other words, as a Trekkie is to Star Trek, a Sawist is to the Saw films.
Often hated for being fans of a franchise which some argue has worn out is welcome with goriness and sequels, and often imagined to be 'sick' for liking a series that's been labeled 'torture porn', Sawists are a rather rare breed.
As in, if you go out on the streets and ask people, you'll probably find lots of fans of Star Wars, lots of fans of Star Trek, lot of fans of Harry Potter, et cetera, but only now and then do you find a particularly devout Saw fan, or Sawist. They're an interesting bunch, that's for sure.
Sawists can go into categories, the most prominent being 'Gordonites', the fans that believe Dr. Gordon from the first Saw lived after cutting off his foot and crawling away. They usually have all sorts of theories about it about the subject causes much flame wars on boards such as IMDb.