If a file does not download, have you tried inspecting the HTTP::Response object you receive from the ->get() call?

my $response = $mech->get($url);
open my $output, '>:raw', '/tmp/output.jpg';
print { $output } $response->decoded_content;
[download]

Edit: You might need to touch the ->content of the browser first so everything has time to initialize first:

my $response = $mech->get($url);
my $c = $mech->content; # Dummy request to initialize everything
open my $output, '>:raw', '/tmp/output.jpg';
print { $output } $response->decoded_content;
[download]

Corion,
This code did the trick for image files but not for PDFs. I also noticed that it works only for simple urls in the page. It did not work for me when the images are displayed using JavaScript.
I was hoping to find a way to block the browser from displaying the documents by using something like the Content-Disposition option.

Content-Disposition: attachment; filename=$filename
[download]

This has worked very well with WWW::Mechanize.
Thank you.

Your problem statement seems to continously change. I don't see/understand how you can get from "image download using its URL" to "image displayed using Javascript" without changing the problem entirely.

Maybe you can come up with a small, self-contained program that reproduces your problem, and also shows the response you receive and also tell us what parts you have already investigated, instead of letting us guess. That way, we can more easily reproduce what you see and maybe suggest better approaches.

If an image gets created using Javascript, you will have to fetch the image data from the browser memory, most likely by using some Javascript to fetch that image data. You can run arbitrary Javascript on a page using ->evaluate_in_page.