Okay, looks like I figured it out...
<?php
// Create image instances
$src = imagecreatefromjpeg('chopme.JPG');
$dest = imagecreatetruecolor(100, 25); //if original is 100X50
// Copy
//imagecopy(resource $dst_im , resource $src_im , int $dst_x , int $dst_y , int $src_x , int $src_y , int $src_w , int $src_h)
imagecopy($dest, $src, 0, 0, 0, 0, 100, 25);
// Output
header('Content-Type: image/jpeg');
imagejpeg($dest);
?>
Now I just have to figure out how to add it to the initial image generation script so that the chopped image is saved.