Well of course it would be discrimination, just like when I discriminate against Heineken in favor of Shiner Bock. The question is whether your discrimination would be illegal. The Americans With Disabilities Act certainly prohibits much employment discrimination against disabled persons, and mandates “reasonable” accommodations for their disabilities. If the amputee could not perform the job even with any reasonable accommodation, there would be no violation of the federal law.
On the other hand, my limited knowledge of the ADA gives me the impression that it would be an open question whether you violate the law by refusing to hire the one-legged letter carrier because the dude seems completely bonkers. And lord knows we don’t want any more nutjobs working for the Postal Service. 
