[PsYcNeT]

Lots Of Blood:

DOOM (SP)
Wolfenstein: The New Order (SP - cheap!)
Dying Light (SP/MP - cheap!)

Blood-ish:

Battlefield 1 (SP/MP)
Far Cry 4/Primal (SP/Co-op)
Rainbow Six: Siege (MP only)

Not Really Bloody At All:

Titanfall 2 (SP/MP)
Overwatch (MP Only)

Are games I would recommend.