Under -> Other homegroup actions you will see the Leave the homegroup… link, click on that link:
Click on Leave the Homegroup and Finish:
UPDATE: The HomeGroup icon is back, so this fix listed below isn’t the answer, just a 2 day fix. I will research another solution, test and advise.
I put Windows 8.1 Pro in production last year and noted a recurring issue. On boot up, the Homegroup icon would mysteriously add itself to the desktop.
Obviously a “bug”, and found this fix:
Go the Control Panel, Click on Network and Sharing Center. On the left hand column, click on -> Change advanced sharing settings.
Select -> Use user accounts and passwords to connect to other computers in the HomeGroup connections. Click on -> Save Changes
So far so good, no more HomeGroup icon on the desktop.