MY GAME IDEA

Have you played Desert Nightmare? The first few scenes sound similar to your idea.

One crucial aspect that help make a good horror game is to give the player logical answers to the questions he may ask himself throughout the game, yet still keep some mystery at the end or shake his beliefs by casting doubt on the truthfulness of the earlier answers.

For instance, make sure there is a rational explanation for questions like these: How did the note written in blood reach the character? Why is it addressed to her? Why is she alone when she wakes up? How were the mutants made? Why did they escape? etc. And then you subtly hint that the character is a mutant herself and that what she experienced during the game is an illusion. (obviously, don't use this idea, it's lame).

EDIT: For the Saw-like idea, the first Saw movie I think is very good. It conceals information from the viewer and shoves it in his face at the end, which makes it striking and memorable.
The following Saw movies (2 and 3 at least, I haven't watched the other ones) focus too much on gore to try to shock and scare the audience and lost what made the first movie great. And unfortunately watching any of the sequels first spoils all the impact of the first movie.