A Japanese edition BD for theatrical version was released Dec 2011.
http://www.yesasia.com/us/my-sassy-girl-blu-ray-japan-version/10256279 75-0-0-0-en/info.html
I am not aware of the existence of any BD editions of the Director's Cut. (137 mins)
This movie is already on Blu Ray!!! The disk have been released in stores from Korea and Japan, maybe you can get a copy on the internet, in an Asian stuff on line retailer.
What I don't like about it, is that the BR edition has the "Suitable for all ages/International" cut from the movie... they cut out a lot of funny and important parts. My suggestion to you is to forget a about the Blu-Ray copy and try to get the "Director's cut" edition.