There are several synonyms for the phrase "dash someone's hopes," which means to disappoint or frustrate someone's expectations. One similar phrase is to "crush someone's dreams," which suggests a deeper level of disappointment and loss. Another synonym is to "shatter someone's illusions," which implies that someone's beliefs or perceptions have been completely shattered. "Dishearten" and "discourage" are also similar in meaning, as they suggest a loss of hope or motivation. Additionally, "disappoint," "let down," and "fail to live up to expectations" all convey a sense of unmet expectations or unfulfilled promises. Overall, there are many ways to express the idea of dashing someone's hopes, each with their own subtle differences in meaning.