"伤害之外又加侮辱" can be translated into English as "to inflict injury and then add insult to it" or more naturally, "to add insult to injury".
The latter is a well-known idiomatic expression in English that precisely conveys the meaning of worsening an already bad situation by adding a further humiliation or injury. While the first translation is more literal, the idiomatic expression "to add insult to injury" is the more commonly used and natural-sounding phrase in English.