On this page of the guide, you will find a description of all the ways in which Max can die. Remember that the game features the "death rewind" option, which you can use if you die by accident.
Considering the content of this page, a spoiler warning is in order. Below, you will read about important choices and situations that happen during The Quarry's storyline. For obvious reasons, we had no way of avoiding spoilers, but we tried to describe the storyline as vaguely as possible, and only point to specific situations.
Max's death is only possible in one case. For this to happen, you must do the following. In chapter 9 you must kill the transformed Chris, this will free Max from the curse. When you come to play it, choose the "swim to shore" option. There the boy will be bitten and die on the spot. However, if both he and Laura survive, you'll get the Should've Gone to the Motel achievement at the end.