As the series goes on, it becomes clear that despite his purported philosophy about life and his "games", Jigsaw breaks his own rules again and again, or doesn't really believe in them at all.
He claims to despise murderers and denies that he is one. Putting aside the fact his games are pretty much universally intended to kill the people that fail them, the games are often Kaizo Traps that trick his victims into dooming themselves, or else his hints to them on how to win are so vague and cryptic that they're useless. Furthermore, his moral compass is anchored by the fact that his victims die because they lack the "survival instinct." Ergo, it is ultimately their fault. Yet he frequently includes innocents in his games, like Lawrence's wife and daughter in the first movie and Eric's son in the second, placing them in danger and usually resulting in death, with no way to save themselves. This hypocrisy is lampshaded when Eric states that his son has done nothing wrong and doesn't deserve to be part of the game just to punish him; Jigsaw doesn't deny this nor explains it. To quote CinemaSins on this moment:
"Um, no. Yeah, he's a murderer. By law. In like, every state and every civilized country and probably even Idaho."
Additionally, some of his games can only be won by murdering someone else, running directly against his core belief. For example, in the first movie, Amanda has to free herself from the infamous reverse bear trap by cutting open the stomach of a sedated man who could barely react and couldn't save himself from her, so the game was practically guaranteed to produce at least one death. Saw VI runs entirely on this, as Easton has to make choices that result in the deaths of others, and the first game was impossible to lose because of Hank's history of smoking, age, and diminished lung capacity. Even if Easton tried to throw the game, he would have won simply because it's very hard for people to hold their breath repeatedly.
He specifically states he's never tried to kill anyone intentionally. Yet, in the first movie, he slashes Tapp's throat and tricks Sing into triggering a row of rigged shotguns that kill him. The two were primarily interested in bringing Jigsaw to justice and saving lives.
He tests William Easton because of how arbitrarily he chooses whether or not people die in his duties as an insurance executive. He does this by arbitrarily having innocent people killed just so William is forced to choose who lives and who dies. That said, this example could be due to Hoffman running that particular game; we never know how much or little his apprentices altered the game designs.
Despite his claims that he actually wants his victims to win their games, when it looks as though Jeff is going to make the correct choice and pass the final part of his test, Jigsaw doesn't look particularly overjoyed. In fact, he looks disappointed. He's correspondingly thrilled when Jeff fails as it means he gets to go through yet another game.
Likewise, when Art, somehow, actually wins his game, Jigsaw throws him in another in which his fate is out of his hands. Furthermore, there's an implication that Jigsaw would have kept running him through games until he inevitably died.
He despises people like Adam and Michael for being "voyeurs" who profit off of spying on people and selling information. That's pretty fucking rich coming from a guy who not only also stalks and spies on others, but puts them through true hell for personal secrets he's learned by spying on them.
If a test malfunctions, John usually just leaves the person to their fate. Most notably in the first movie, where Adam loses the key to his chain, something which John could not have foreseen. John does nothing and leaves Adam to die. Initially, his moral compass was more functional, as he would intervene if something went wrong, like when he saved Logan in Jigsaw. He acted out of a belief that every person should have a fighting chance in their games. Logan didn't have one due to the fact that John had accidentally overdosed him. He also realized that Logan's transgression was a simple accident and as such it wasn't really fair. However, he grew out of that by the events of the first movie.
John tells Logan that they can never act out of anger or vengeance, Logan himself having taught John that since his mislabelling of John's x-ray was an accident and he didn't deserve to die for it. Yet his very first victim was the drug addict who caused his ex-wife to have a miscarriage. He also targeted Mitch for causing his nephew's death, blackmailed Hoffman into becoming an apprentice, had Easton targeted for turning down a cancer treatment that could have saved John's life, and left instructions for Lawrence to take care of Hoffman in case he tries to murder Jill. Though in the case of Cecil and Mitch, those were clearly before John saved Logan.
In the Saw VI flashback to III, when Hoffman is roughly lugging around an unconscious Timothy's body, John scolds him that he's a human being. Considering what insidious torture device John has planned for the man...
Although, it's possible that he meant that Hoffman shouldn't be reckless so as to not accidentally kill Timothy before Jeff's trial begins.
Considering that one of the biggest precipitating factors in John becoming Jigsaw was the death of his unborn son at the hands of a junkie, John putting Jeff's daughter in a life-threatening situation to test him when Jeff had already had his own son taken from him before his time by somebody's else mistake (just like John) comes across as John really only caring about his own pain. His Relative Button concerning Jill is also this, because one of John's favorite methods during games is to involve the subject's family members, regardless if said loved ones are guilty of anything or not, which he does in the following: the first movie with Lawrence's wife and daughter, II with Eric's son, III with Jeff's wife and daughter, VI with William's sister (Hoffman set that game up, but John is the one who picked out William and likely came up with much of the details for his game) and 3D with Bobby's wife).
He scolds Hoffman for not giving Seth (a domestic abuser) a chance and that everyone he tests has a chance to live. Never mind that he later didn't give Rex, who's very similar to Seth, a chance to escape from his trap, as he was pierced through his vital areas with spikes that his wife Morgan removed.
He expresses contempt for suicidal people, whom he sees as wasting the precious gift of their lives (which he claims he had been denied from), despite the fact that he himself tried to take his own life after his diagnosis.
Logan Nelson:
Logan has the nerve to judge other people for their sins when he essentially, though not maliciously (it was a genuine mistake) caused John to die a slow, painful and altogether avoidable death. He was also put into a Jigsaw game himself for that, then survived the experience only because of the mercy of the man whose life he doomed.
He's told by John "We can never come from anger, or from vengeance," as he learned from erroneously putting Logan into a trap. Ten years later, he kills Edgar and Halloran for their supposed role in his wife's death, after both of them passed the tests they were given. For the latter case, though, Halloran arguably failed when he attempted to get Logan killed in the trap.
Though he states that he's only going after Dirty Cops, William Schenk killed and then flayed his accomplice to use him as a body double. He doesn't seem to reflect on how this puts him in a similar league to the officers he's targeting.
