As revealed at the end of Saw 2, knowing his time is near, Jigsaw takes on an apprentice. The apprentice is Amanda Young – the Beartrap girl from SAW, and the “survivor” from SAW 2.
Jeff is an anguished man, who grieves and misses his young son that was killed by a driver in a car accident. He has become obsessed for revenge against the man and reckless with his wife and daughter. When Dr. Lynn Denlon, who has troubles with her marriage, is abducted by the deranged Jigsaw’s apprentice Amanda, she is brought to a gruesome warehouse to keep John Kramer alive in spite of having a terminal brain tumor. Amanda puts a necklace gadget full of explosives around Dr. Lynn’s neck connected to John Kramer’s life support system, and tells her that if he dies the device will explode. Meanwhile, Jeff is submitted to a sick game of forgiveness with surprising dark consequences. (source: IMDB)
There is an inherent problem with Amanda’s traps. They can’t be solved. While Jigsaw did what he did to try to make his victims appreciate life. Amanda is just a psychotic bitch, using Jigsaw’s devices to her own will. She sees these people not as subjects to be redeemed.. but deserving of death, and she is the reaper.
With most trilogies.. SAW 3 jumps the shark, and turns an interesting franchise into a bunch of movies to not be taken seriously. Just a bunch of “Hey, how can we kill this guy off” with no rhyme or reason behind it.