Just gentle reminder to yourself and everyone else to to please keep discussions about mods to the Gaming Mod thread. The purpose of this thread is compile discussions, recommendations and tips and questions together to make finding them easier in the event someone else has a similar query rather than have that information scattered elsewhere on the site. Please don't make new threads, just post the query here instead. No biggie, I've merged the threads together now.
Anyway, in answer to your question, whether one has to load an old save or not depends on the nature of the mod itself. Mods to improve textures, graphics, the UI or sound, usually not because that's just changing something that's already there in the base game. However, if the mod adds characters, animations, questlines, items or environments, then removing the mod will will remove those and may may cause problems as those characters, items, animations, questlines or environments will no longer exist. So if you remove a mod that adds a certain weapon, that weapon will disappear, but is unlikely to cause a crash or warrant a re-load of an older save, but if your mod adds a player home and you remove that mod, a save from inside that player home will not load properly.