If I uploaded a file to a website, is it saved somewhere in the Safari application? Or elsewhere in the computer?
In general, once a Unix file is deleted, it's deleted. That said, there are certain 3rd party utilities that may be able to scour your HD for file signatures that match the file format you used (PDF?) and recover the file. Here is a review of the 3 biggest titles for you to choose from:  http://www.techrepublic.com/article/3-data-recovery-applications-for-os-x/ 

One issue that is critical: Stop using the Mac.  The more you use it and save/alter files, the more likely the disk sectors that contained your scan will get overwritten.