When you have young children it's easy to loose your cool in the name of discipline. But as most people know, hitting or even yelling is not an effective way to change behavior and has negative long-term consequences. This scenario mirrors dealing with children and illustrates effective and ineffective ways of modifying behavior.

To the player: You made minor mistake and breached character. Perhaps there are some in-game methods of venting, such as praying while still in character. Or just swear like a dwarf a little in the room, while still in character.

To the immortal I have three points. First, see this from the player's perspective and remember that everyone is fighting the good fight and doing the best they can. There was a lack of empathy in your response. Second, you responded to someone breaking character by breaking character yourself. If you want to encourage players to remain in character you shouldn't be breaking character, and this could have been dealt with in a positive fashion by remaining in character. Third, a roleplaying violation, especially when there are no PC victims, should not result in ROTD and a slay. A punishment this severe was often reserved for egregious rules violations, such a permas, multicharing, and other forms of cheating.

To Destuvius, you're in a tough spot. I would view all parties as your children. They both did something wrong, and both should learn something from the event. Ask yourself what the desired outcome is and how you achieve this. A severe punishment overlooks the forest (the overall health of the MUD and playercount) for the tree (a minor, and based on the information presented, victimless violation). But, you need both the immortal and the player to keep the game healthy.

How would I have handled this? Well, it's easy for me to play a Monday morning arm-chair quarterback, so here goes...
I would have taken away the character's voice, either through a very long garble or the mute edge if I felt it was warranted.