Is COD black ops alright for a MATURE 13 yr old?

my mom thinks im not old enough for this but she got it for me anyway shes considering getting rid of it due to the graphic violence but considering i play bfbc1+2 aliens vs predator and halo (ik its minor) im wondering why in avp u can rip peoples heads off with a spine still dangling on it with gore going EVERYWhERE im just comfused... i understand that war is real and violent...im not 6... but she seems to think so