“丢脸的”的英语可以翻译为：humiliating，humiliatory ...

她儿子丢脸的事让她很难过.Her son's disgrace broke her heart.这不是丢脸的事.There's nothing to be ashamed of.撤销机场对现任州长来说将是件丢脸的事情。To cancel the airport would mean a loss of face for the present governor....