The movie does not depict Edward's origin story in detail, but it is suggested that his creator, an elderly inventor, was working on a project to create a human-like being but died before he could finish. The creator left Edward with scissor blades for hands, which are implied to be a part of his unfinished design.
There is no indication that Edward was made from human parts or that he is a Frankenstein-esque creature. He is more of a misunderstood, incomplete creation with a unique and tragic story.