why does amanda work with jigsaw ?

cuz she keeps cutting herself.

Well he appeared to her, and possibly explained his philosophy to her. After the trap, she cries and says he helped her. Due to his trap, she realizes how much she wanted to live, and is grateful to be alive.

Long post. Sorry
But, she's not mentally healthy. And she doesn't have much self-worth. She was verbally and physically abused by her father growing up, and apparently she had no mother in the picture. As the writers say, Amanda is someone who needs something exterior to keep her grounded. So drugs became her outlet, which ended up causing trouble. When John came to her, explained himself and wanted her help, she probably felt grateful for his test, and thus was willing to help him.

After a while, John became her new "drug." He was the person who gave her new appreciation for her life, least more than she had. And with helping him, he also gave her a goal and purpose in life, and a bit more power as the writers said.He kept her grounded after John told her that her drug days were over. So then she became very attached to him, to the point of jealousy and possessiveness, as we see with Lynn. But with John having cancer, and on the verge of dying soon, Amanda was of course not happy about it, and now that he won't be around for her much longer, she's resorted to cutting herself again.

So with all her issues, we hear her feelings. As she says in II, she claims everything is a lie, and that nobody ever really changes, or is reborn. So her tests were unpassable, because she felt even if they succeed, they still will not have changed. So she just sets up unwinnable traps to kill them and put them out of their misery, so to speak.