I think you're confusing a few things here.
First, to get the mirror, you have to deal with the family in the Macalania Woods. That's the father and mother and son near the savepoint. That's to get the mirror, which helps you build all of the Ultimate Weapons.
But to get Tidus' weapon, you have to do the chocobo race in the calm lands. When you win the race, you then want to go northwest to get to where it is. That has nothing to do with a savepoint.
http://www.bellaonline.com/gaming/strategy_lib_ffxwalk_ut.html