Here is the full list of all 46 Saw achievements.
Killed a Collared Minion with a collar detonation
Release Amanda from her Trap
First kill with a Crutch
Four kills with a Bat
First kill with a Scalpel
Unlocked First Door
Used Health Syringe for the first time
Find your first Patient File
Kill first Minion
Five kills with a Pipe
Fought first NPC
Find your first Asylum File
First encounter with Pighead
Unlock First Container
Complete Reverse Bear Trap
Died three times
Release Jennings from his 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
Kill 10 Minions
Kill 20 Minions
Used 20 Health Syringes
Idle for five minutes
Five kills with a Mannequin Arm
Five kills with a Nail Bat
Five kills with a Mop Handle
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 5 locked doors
Unlock 20 locked doors.