肃清 is heavy, formal political/military register. Common collocations:
肃清流毒 (purge harmful influences),
肃清残敌 (mop up the remnants of the enemy),
肃清贪腐 (root out corruption). Implies thorough, top-down cleansing — don't use it for simply 'cleaning up' (that's
清理 qīnglǐ).