"Giving someone his walking papers" is a colloquial phrase that means to dismiss an employee or end a relationship. When looking for synonyms to replace this phrase, one might consider using terms such as "firing," "letting go," "terminating," or "separating." Other phrases that could be used include "sending someone packing," "showing someone the door," or "letting someone go with immediate effect." These alternative phrases communicate a similar notion of ending a relationship or employment, but might offer a different connotation or tone depending on the context. Ultimately, the choice of synonym will depend on the writer's intention and the desired impact on their audience.