YOU SAID:

my mom has killed the cat in the back

INTO JAPANESE

私の母は後ろで猫を殺しました

BACK INTO ENGLISH

My mother killed the cat behind

INTO JAPANESE

私の母は後ろの猫を殺しました

BACK INTO ENGLISH

My mother killed the back cat

INTO JAPANESE

私の母は裏猫を殺した

BACK INTO ENGLISH

My mother killed the back cat