I've recently started using mac os. Do I have to buy the game again only for mac? or is it possible to download it from somewhere?
Look at your Battle.net "Game Accounts" section. When you click on Diablo III you should find a nice selection of game clients to chose from. These include various different languages as well as Windows and Mac. You don't have to pay extra.
What you can do is download the Mac client from battle.net, start the installer and the moment the red bar in the "setup" phase changes to orange, stop the installer, copy over your Data folder into the newly installed Diablo III folder (select OK to overwrite), and then re-run the Diablo III Launcher inside your Diablo III folder. It will patch itself and you'll be up and running faster than you otherwise would since you don't have to download gigabytes of data all over again.