Say your local website is host-a.com, and your image is mirrored as http://host-b.com/img.gif, http://host-c.com/img.gif and http://host-d.com/img.gif.
Then you can set up a script like this on host-a.com:
$img = file_get_contents('http://host-b.com/img.gif')
or die('Cannot get image');
Save this in, say, mirrored-img.php on host-a. Then your web pages can use <img src="http://host-a.com/mirrored-img.php"> to get the file from one of those three sites.
Adapt accordingly. Ideas: (1) Use GET variables to make that script grab any named mirrored file; (2) Build some intelligence into that script to discover the file type and output suitable content-type headers; (3) Randomise the order in which the mirroring hosts are contacted so you get load-balancing, sort of.
You still have to set up the mirroring yourself, of course.