When it comes to ending someone's employment, there are a number of ways to phrase it without using the idiom "give someone his walking papers." Some alternatives include "terminate," "dismiss," "fire," "let go," "sack," "axe," "release," "sever ties with," and "end the employment of." Each of these options conveys the same basic idea of ending someone's employment, but they may carry slightly different connotations depending on the context. Ultimately, the choice of wording will depend on the situation and the desired tone of the message.