A simple method (if using Linux based server) is to use the exec command and to run the split command:
exec('split Large.tar.gz -b 4096k SmallParts'); // 4MB parts
/*    |     |            |      | |
      |     |            |______| |
      App   |                 |   |_____________
            The source file   |                 |
                              The split size    Out Filename
*/
See here for more details: http://www.computerhope.com/unix/usplit.htm
Or you can use: http://www.computerhope.com/unix/ucsplit.htm
exec('csplit -k -s -f part_ -n 3 LargeFile.tar.gz');
PHP runs within a single thread and the only way to increase this thread count is to create child process using the fork commands.
This is not resource friendly. What I would suggest is to look into a language that can do this fast and effectively. I would suggest using node.js.
Just install node on the server and then create a small script, called node_split for instance, that can do the job on its own for you.
But I do strongly advise that you do not use PHP for this job but use exec to allow the host operating system to do this.