To delete any branch from VSO, you have to enable Alternate Authentication Credentials
Open VSO web browser.
Click on your name in the top right
Click on My Profile
Click on Credentials
Configure Alternate Authentication Credentials
Now open Visual Studio
Connect VSO.
Click on Team Explorer
Click on Home
Click on Branches
Click on Actions
Click on Open Command prompt
Now run below command to delete branch from GIT
git push origin --delete <Branch Name>
Open VSO web browser.
Click on your name in the top right
Click on My Profile
Click on Credentials
Configure Alternate Authentication Credentials
Now open Visual Studio
Connect VSO.
Click on Team Explorer
Click on Home
Click on Branches
Click on Actions
Click on Open Command prompt
Now run below command to delete branch from GIT
git push origin --delete <Branch Name>