Is it a sin to dismiss a negligent employee or deduct from their salary, knowing that their negligence harms my position as the facility manager?

Those in charge of others' affairs must rule with justice and fulfill their trusts, as Allah Almighty commanded in verse 58 of Surah An-Nisa. The ruler is responsible for his subjects and must punish the wrongdoer and reward the doer of good. If he misbehaves and wrongs the people, he will have betrayed the trust and borne the injustices of his subjects, and seeking favor with his employer will not benefit him.