Expanding on a comment below about using munpack to extract attachments, here's a lazy person's function that extracts attachments from mail with $msg_number from $mailbox and writes them to $dir. It returns an array of filenames or false if there are no attachments. 

function writeAttachmentsToDisk($mailbox, $msg_number, $dir){
  
  if (!file_exists($dir)){
    mkdir($dir);
  }
  $filename = "tmp.eml";
  $email_file = $dir."/".$filename;
  // write the message body to disk
  imap_savebody  ($mailbox, $email_file, $msg_number);
  $command = "munpack -C $dir -fq $email_file";
  // invoke munpack which will 
  // write all the attachments to $dir
  exec($command,$output);

  // if($output[0]!='Did not find anything to unpack from $filename') {
  $found_file = false;
  foreach ($output as $attach) {
    $pieces = explode(" ", $attach);
    $part = $pieces[0];
    if (file_exists($dir.$part)){
      $found_file = true;
      $files[] = $part;
    }
  }
  if (!$found_file){
    //echo ("\nMail.php : no files found - cleaning up. ");
    // didn't find any output files - delete the directory and email file
    unlink($email_file);
    rmdir($dir);
    return false;
  }
  else {
    // found some files-  just delete the email file
    unlink($email_file);
    return $files;
  }
}