cat BIG_FILE.tar.gz | ssh user@192.168.1.12 "tar xzf - -C /home/user"
This magic command uses the network to only transfer the file and as it reaches the target computer it starts getting decompressed straightaway. Minimum traffic, no temporal disk usage.
tar czf - /home/user | ssh sam@192.168.1.15 "cat > /my/place/to/store/BIG_FILE.tar.gz"
This creates the compressed file on the fly and writes it in the remote machine without intermediate copies.