Linux Mint does not provide the option to remove a ppa.

If you try it, this will be the result:

sudo add-apt-repository --remove ppa:somePPA/ppa
Usage: add-apt-repository [options] repository

add-apt-repository: error: no such option: --remove

But you can still manually remove a ppa in Linux Mint by removing the file that defines it. All ppa are defined in /etc/apt/sources.list.d . So you can do the following:

# find the correct ppa file to delete by listing all ppa files:
ls /etc/apt/sources.list.d

# delete the ppa that you would like to remove:
sudo rm /etc/apt/sources.list.d/some-ppa-to-remove.list

# update
sudo apt-get update

And that is it, you should now have removed the ppa.