Virtual Server with no Snappoint function: How do I make a full-backup of the running system?

Question

So I'm currently experimenting with a couple of uni servers. All of them have no option of creating snappoints in the vSphere Client. So I'm left to search for a backup solution in case the experimenting makes everything kaput.

Seeing as that I'm a linux beginner, what options are there for me to make a full backup of the currently running Ubuntu 16.04 for emergency cases when everything goes kaput.

To clarify: I have ssh access, I have a terminal access with putty. I can log with Filezilla via sftp and see all the folders. I have root access. What I DON'T have is physical access to the machine.

root@xxx:~# df -h
Filesystem                           Size  Used Avail Use% Mounted on
udev                                 3.9G     0  3.9G   0% /dev
tmpfs                                797M   18M  780M   3% /run
/dev/mapper/vcac--ubuntu16--vg-root   15G  1.9G   12G  14% /
tmpfs                                3.9G     0  3.9G   0% /dev/shm
tmpfs                                5.0M     0  5.0M   0% /run/lock
tmpfs                                3.9G     0  3.9G   0% /sys/fs/cgroup
/dev/sda1                            472M   58M  391M  13% /boot
/dev/mapper/data-disc1                50G   33M   50G   1% /net/xxx/disc1
tmpfs                                797M     0  797M   0% /run/user/0

To clarifiy, I want to do a backup of this output. Obviously not What's been mapped, but what is used.