I'm unaware of any way to do this if the interim result you need is a flat file that can be used by other applications other than the editor. If you want a flat file to be produced, you will have to update it from the change point to the end of file, since it's really just a sequential file.
But the italics are there for good reason. If you can control the file format, you have some options. Some versions of MS Word had a quick-save feature where they didn't rewrite the entire document, rather they appended a delta record to the end of the file. Then, when re-reading the file, it applied all the deltas in order so that what you ended up with was the right file. This obviously won't work if the saved file has to be usable immediately to another application that doesn't understand the file format.
What I'm proposing there is to not store the file as text. Use an intermediate form that you can efficiently edit and save, then have a step which converts that to a usable text file infrequently (e.g., on editor exit). That way, the user can save as much as they want but the time-expensive operation won't have as much of an impact.
Beyond that, there are some other possibilities.
Memory-mapping (rather than loading) the file may provide efficiences which would speed things up. You'd probably still have to rewrite to the end of the file but it would be happening at a lower level in the OS.
If the primary reason you want fast save is to start letting the user keep working (rather than having the file available to another application), you could farm the save operation out to a separate thread and return control to the user immediately. Then you would need synchronisation between the two threads to prevent the user modifying data yet to be saved to disk.