From winter season 2015-2016 onwards several shops will be open on Sunday. So in winter time, no big problem to find your groceries on Sunday. Summer time is a slightly different story. In summertime only the Billa shops are open.
There’s a Billa in Kaprun (Umfahrunggstrasse 4 – 5710 Kaprun) (that’s the closest one) : location here.
There’s a Billa in Zell am See (Flugplatzstrasse 54 – 5700 Zell Am See/Schüttdorf) : location here.
Both stores are open on Sunday morning between 9AM and 13AM.