There is really not much suspense in SAW series, because you pretty much know what to expect. If you have the gutts for true suspense, go with some Japanese horror movie, like Audition (1999) or Gozu (2003).
You can watch zodiac, usual suspects and scream series. These are some very good movies and also you can watch i know what you did last summer. If you need a site name i can tell you that also.
I'd say Devil, It doesn't have too much horror or gore, but it builds so much suspense for you to find out who the "Devil" is in the Elevator.
Although older, I found "Untraceable", "When a Stranger Calls", "The DaVinci Code", "Angels & Demons" & "The Bone Collector" to be quite suspenseful.