From the very beginning their two characters clashed and the relationship had only been deteriorating.

clashed 是动词 clash 的过去式。clash 本意是"金属撞击声"，引申为"冲突、不协调"，指两种事物或观点之间产生矛盾或对立。在句中表示两人性格从一开始就存在冲突。