If you have a sshd running on the machine with the big tar archive and an ssh client on the one you are copying to, then you could do this:
ssh machinewitharchive "cat /path/to/file.tar.gz" | tar xz
: Actually it would work the other way as well (ssh client on the machine with the big file and ssh server on the receiving machine):
cat /path/to/file.tar.gz | ssh machinereceivingarchive "tar xz"
Don't you just love tar pipes?
: Another option would be to use network shares. Then you could mount the directory containing the big archive on the receiving machine and just do a regular "tar xf file.tar.gz". NFS or SMB/CIFS would be obvious options for this. Alternatively could still use ssh via SshFS/Fuse or perhaps fish:// in a file manager like Dolphin and then use Ark to unpack.