Yeah Jigsaw died in like Saw III, but the movies generally pick up RIGHT where the last ones left off. The bulk of Saw VI takes place probably a week or so after his death, so his influence is still all over the place. When he died, he had a few things already in place with a few pawns carrying out his wishes, so his stuff is still being carried out. Through newly filmed flashbacks, he had a pretty sizable role in Saw VI.
Saw III and IV took place simultaneously, which was pretty wild. It makes keeping the storyline straight a challenge, but it does make sense and Jigsaw\'s motivations are pretty compelling. He didn\'t generally want to kill anyone, just punish people, test them and give them the tools to realize and change whatever was so bad about their personality... The couple of people he\'s groomed to replace him, he\'s not sure they always share the same intentions so there\'s always that under current of whether and how Jigsaw will be testing them as well.