Yes, indeed you can.
To do this, we use a command line utility (which should be already installed) for network manager called nmcli.
To disconnect
you need to run the following command:
nmcli dev disconnect iface eth0
Note: You need to make sure that the iface value for the connection is eth0, you can do so by taking a look at the status of all the devices:
nmcli dev status

Note that, in this case, eth0 is connected, hence the iface value is eth0.
To connect again
you need to know the uuid of the connection. Run the following command:
nmcli con
and note the uuid of your connection.
Then, to connect to that connection, run
nmcli con up uuid <uuid>
where <uuid> is the uuid you noted from the previous command.