Well, if we consider a fanfiction where Jon Snow kills the Mountain, it could be a great display of Jon's skills with his sword, Longclaw. The Mountain is a formidable foe, so for Jon to defeat him would require not just physical strength but also strategic thinking. It could also be a moment of vengeance for some wrong the Mountain has done in the fanfiction world.
In many fanfictions, characters are put in situations that deviate from the original storyline. When it comes to Jon Snow killing the Mountain, this could be part of a larger narrative. For example, it could be a turning point in a war where Jon's victory over such a powerful enemy gives hope to his side. It might also change the political dynamics in the fictional world. The author could explore how this act affects Jon's relationships with other characters, like his friends in the Night's Watch or potential allies in the Seven Kingdoms. There could be moral implications as well, as killing is not always a simple act in the complex world of Westeros.
In fanfiction, Jon Snow killing the Mountain could be a very interesting plot twist. It might show Jon's growth and his ability to take on powerful adversaries. Maybe it's set in an alternate scenario where their paths cross in a more direct combat situation.