dégraisser

Literally to remove fat or grease — from a cut of meat, a sauce, or a stained garment (dégraisser une veste at the dry cleaner's). Very commonly extended, especially in business and political journalism, to mean cutting staff or costs (dégraisser les effectifs).

• Il faut dégraisser le bouillon avant de le servir. — The broth needs to be skimmed of fat before serving.
• Le pressing va dégraisser cette tache sur le col. — The dry cleaner will remove this grease stain from the collar.
• L'entreprise prévoit de dégraisser ses effectifs cette année. — The company plans to cut its workforce this year.

The workforce-cutting sense is everywhere in economic news but is genuinely informal/euphemistic — using it in a formal HR document would sound flippant about job losses; réduire les effectifs is the neutral register.

• politics "Dégraisser le mammouth" — Phrase used by French Education Minister Claude Allègre in 1997 to describe cutting staff in the sprawling national education bureaucracy — it became a widely quoted soundbite during his standoff with teachers' unions.