When searching for synonyms for the phrase "cruel act," there are several words and phrases that come to mind. One option could be "inhumane behavior," which refers to actions that are lacking in compassion or kindness. Another option could be "barbaric deed," which suggests a sense of brutality or savagery in the action. Another alternative could be "vicious act," which implies a sense of maliciousness or aggression. And yet another option could be "callous action," which suggests a lack of empathy or concern for others. Ultimately, the choice of synonym depends on the context of the situation and the writer's desired tone.