No, that won't delete your save file. It will start a new game, but you will not be able to save the game. You'd cannot have two separate save files.
There is no way for your friend to play a new file without you having to delete your existing file. If you want to delete your file, hold down the Up, B and L buttons at the same time and select 'yes' when the games asks you if you want to delete your file.
The only way that you can both play the game without you losing your save file is for your friend to get their own copy of the game.