As soon as you start Mullvad VPN the Internet connection is not working. Although Mullvad shows a working connection and ping is working, no websites can be reached.
This seems to be an issue on Arch Linux.
Do this (according to the brilliant Mullvad support):
sudo systemctl enable systemd-resolved
sudo ln -sf /run/systemd/resolve/stub-resolv.conf /etc/resolv.conf
sudo systemctl start systemd-resolved
sudo systemctl restart NetworkManager
Works for me and my clients.