"Gives the ax" is a common expression used to describe a decision to terminate someone's employment. However, there are several synonyms you could use to avoid using this phrase. One alternative could be "to lay off" or "to let go," which are friendlier alternatives to use in the workplace. Another option could be "to dismiss" or "to terminate," which are more formal and serious phrases. Similarly, you could use "to fire" or "to release," but it's important to remember that the word choice may impact the tone and impact of the conversation. Ultimately, it's important to use language that is appropriate and professional when discussing sensitive topics such as employment termination.