Yes, I've been put in that position once. The boss was out of state on vacation, and a chronic troublemaker took advantage of that fact to begin to "poison" a new employee with unfounded rumors, blatant falsehoods, and disrespectful and insubordinate language about the boss. Someone in the office informed the boss of this by text message, and the boss called me with instructions to terminate the offender immediately.
I first asked the boss to give me those instructions in writing, by email, which she promptly did. Then I confronted the offending employee and told her that her services were no longer required. She disputed my authority to terminate her and refused to leave the workplace. I responded by threatening to call the police and have her removed (we have no security department in our company), and proceeded to do so. She immediately changed her mind, gathered her belongings, and headed out the door, loudly mouthing epithets and threats of legal action as she went out the door. End of story.
I'm glad I got my instructions in writing from the boss. I'm also glad I didn't try to physically remove this woman myself. To have done either of these things differently could have made a bad situation much worse.