No, there's no way you can achieve this in Safari. There may be a way on Mac Os with the help of certain scripts but i doubt. Anyway, on safari for windows there's no way at all to open homepage automatically when you open a new tab. The setting here: Edit > Preferences > General > New windows open with , configures safari to open a new window with whatever you set it , can be homepage, empty page, same page.
So if you want to get to your homepage automatically, set that setting to open new windows with homepage if it isn't already. And then you can you can hit Ctrl+N to open a new window which'll open with your homepage...but with what you're asking as to open a new tab with homepage, that's not possible.
So what you can do is drag the home button onto your toolbar and click on it to go to your homepage after opening a new tab.
To drag the home button onto your toolbar, click on view -> customize toolbar. From here drag the home button onto your toolbar and click 'done' .
Besides, if you didn't know, even alt+home shortcut doesn't work on safari for opening the homepage like it works on other browsers like IE,Firefox , Opera etc.