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