"Give someone the ax" is a phrase that is commonly used to mean terminating someone's employment or firing them from their job. However, there are various other synonyms that can be used to express this same sentiment. Some of these include "dismiss", "terminate", "let go", "sack", "pink slip", "axe", "fire", "release", "retrench", "severance", "discharge" and "purge". The language used to indicate the termination of an employee can vary depending on the specific context and tone desired. Nonetheless, regardless of the wording used, firing someone is never an easy thing to do and should always be handled with sensitivity and professionalism.