One way to stop Network Manager from adding dns-servers to /etc/resolv.conf file is to do this:
First open the nm conf file /etc/NetworkManager/NetworkManager.conf:
sudo vim /etc/NetworkManager/NetworkManager.conf
And add this to the [main] section:
dns=none
rc-manager=unmanaged
Save and exit.
reference: https://askubuntu.com/questions/623940/network-manager-how-to-stop-nm-updating-etc-resolv-conf
