Here is the full list of all 46 Saw achievements.
Unlock 5 locked doors
Release Jennings from his Trap
First kill with a Crutch
Five kills with a Mannequin Arm
Unlocked First Door
Five kills with a Pipe
Fought first NPC
Complete Reverse Bear Trap
First encounter with Pighead
Release Amanda from her Trap
Release Melissa from her Trap
Release Oswald from his Trap
Release Obi from his Trap
Release Jeff from his Trap
Kill the Pighead
Complete game using Freedom door
Complete game using Truth door
Unlock First Container
Kill first Minion
Kill 10 Minions
Kill 20 Minions
Used Health Syringe for the first time
Used 20 Health Syringes
Idle for five minutes
Find your first Asylum File
Find your first Patient File
Died three times
Killed a Collared Minion with a collar detonation
Four kills with a Bat
Five kills with a Nail Bat
Five kills with a Mop Handle
First kill with a Scalpel
First kill with a Syringe
Five kills with a Table Leg
First kill with a Shovel
Five kills with a Table Lamp
Five kills with a Hatchet
First kill with a Molotov
First kill with a Scissors
First kill with a Gun
First kill with an Explosive Mine
First kill with a Stun Mine
First kill with a Gas Mine
Stomped first Minion to Death
Stomped five Minions to Death
Unlock 20 locked doors.