An elderly woman describes to her granddaughter where snow comes from by telling the story of a young man named Edward with scissors for hands, the creation of an inventor. The inventor was inspired to make an artificial man due to the anthropomorphic appearance of his other inventions. His final result was a humanlike young boy that had everything except for his hands, but the inventor had a heart attack and died while in the act of revealing a pair of real hands to Edward, leaving him to be "unfinished" forever. Many years later, local Avon saleswoman Peg Boggs, after failing to make profits in her suburban neighborhood, visits a Gothic mansion on a hill. There, she finds Edward alone, and decides to take Edward to her home. Edward befriends Peg's young son Kevin, her husband Bill and later their teenage daughter Kim, the femme fatale of the story.
Peg's neighbors become impressed at Edward's masterful skills at hedge trimming and haircutting. However, two of the townspeople, a religious fanatic named Esmeralda and Kim's jock boyfriend Jim, immediately dislike him. Joyce, a housewife in the neighborhood, suggests that Edward opens a haircutting salon with her. While examining a proposed site, she attempts to seduce him, confusing Edward, who escapes the room in a state of panic.
Wanting money for a van, Jim takes advantage of Edward's ability to pick locks and breaks into his parents' house. The burglar alarm sounds and everyone except Edward escapes, despite Kim's angry insistence that they return for him. Edward is arrested, but released when a psychological examination reveals that his isolation allowed him to live without a sense of reality and common sense. The arresting officer, Allen, befriends the timid Edward, sensing his intrinsic goodness. Meanwhile, infuriated by Edward's rejection, Joyce gets revenge on Edward by claiming that he tried to rape her. This, added to the "break-in", causes many of the neighbors to question his personality. During Christmas, Edward is feared by almost everyone around him except the Boggs family, making him and the family outcasts.
While the family is setting up Christmas decorations, Edward creates an angel ice sculpture from a block of ice. The shavings from the ice create an effect of falling snow, which Kim dances under. Jim calls out to Kim causing her to become distracted, when Edward accidentally cuts her hand in the process as he climbs down a ladder. Jim thinks that Edward had intentionally harmed her and uses this as a advantage to attack Edward in a jealous rage. The situation gets worse when Kevin is almost run over by Jim's drunken friend. Edward pushes Kevin out of the way, accidentally cutting his face in the process, causing witnesses to think he was attacking Kevin on purpose. Edward flees back to his hill-top mansion and the neighbors, gathered up into an angry mob started by Jim, follow him.
Kim heads to the mansion before the neighbors can get there and reunites with Edward. Jim follows them and brutally attacks Edward, who does not retaliate back until Jim hurts Kim. Edward stabs him and Jim falls out a window to his death. Kim confesses her love for Edward, and, to save him, convinces the townspeople that Edward and Jim killed each other in the fight. She tells them that the roof had caved in and shows them a disembodied scissor-hand similar to his. All the neighbors return to their homes, while Joyce is seen feeling guilty and ashamed for making up the rumor about Edward. The elderly woman from the beginning reappears, as she finishes telling her granddaughter the story. It is revealed that Edward is still alive, apparently immortal because he can never age and "creating snow" from his ice sculptures, which fall upon the neighborhood below. The elderly woman reveals to her granddaughter that she is, in fact, Kim. She chooses not to visit Edward because she wants Edward to remember her the way she was in her youth. A young Kim is then shown dancing under the snow falling from the mansion above.