Give/Get the Axe

Definition: if a person gets the axe, he loses his job 

if a plan or a service gets the axe, it is stopped.

If you give someone the axe, you authorize him to stop something or to fire people. 

Examples:

Senior staff are more likely to get the axe because the company can't afford their high salaries.

My research project was the first thing to be given the ax when the new boss took over.