An elderly woman tells her granddaughter the story of a young man named Edward who has scissor blades for hands. As the creation of an old inventor, Edward is an artificially created humanoid who is almost completed. The Inventor homeschools Edward, but suffers a fatal heart attack before he can attach hands to Edward. Edward tries to put the hands on himself, but his blades destroy them. Hurt, Edward cuts the deceased inventor’s face.
Some years later, Peg Boggs, a local Avon door-to-door saleswoman, visits the decrepit Gothic mansion where Edward lives. She finds Edward alone and offers to take him to her home after discovering he is virtually harmless. Peg introduces Edward to her family: her husband Bill, their young son Kevin and their teenage daughter Kim. The family come to see Edward as a kind person, though Kim is initially fearful of him.
The Boggs’ neighbors are curious about their new house guest, and the Boggs throw a neighborhood barbecue welcoming Edward. Most of the neighbors are fascinated by Edward and befriend him, except for the eccentric religious fanatic Esmeralda and Kim’s boyfriend Jim. Edward repays the neighborhood for their kindness by trimming their hedges into topiaries. This leads him to discover he can groom dogs’ hair and later he styles the hair of the neighborhood women. One of the neighbors, Joyce, offers to help Edward open a hair salon. However, while scouting a location, Joyce attempts to seduce him, but scares him away. Joyce lies to the neighborhood women that he attempted to seduce her, reducing their trust in him. The bank refuses to give Edward a loan as he does not have a background or financial history.
Jealous of Kim’s attraction to Edward, Jim suggests Edward pick the lock on his parents’ home to obtain a van for Jim and Kim. Edward agrees, but when he picks the lock, a burglar alarm is triggered. Jim flees and Edward is arrested. The police determine that his period of isolation has left Edward without any sense of reality or common sense. Edward takes responsibility for the robbery, telling a surprised Kim he did it because she asked him to. Edward is shunned by those in the neighborhood except for the Boggs family.
During Christmas, Edward carves an angelic ice sculpture modeled after Kim; the ice shavings are thrown into the air and fall like snow, a rarity for the neighborhood. Kim dances in the snowfall. Jim arrives and calls out to Edward, surprising him and causing him to accidentally cut Kim’s hand. Jim accuses Edward of intentionally harming Kim, but Kim, fed up with Jim’s jealousy, breaks up with him. Edward flees in a rage, destroying his works and scaring Esmeralda until he is calmed by a stray dog. Edward kindly cuts a piece of fur obscuring the dog’s vision. Kim’s parents set out to find Edward while Kim reluctantly stays behind in case he returns. Edward does return to the Boggs home to find Kim there who asks him to hold her, but Edward fears he will hurt her. Jim drives around in a drunken rage and nearly runs over Kevin, but Edward pushes Kevin to safety, inadvertently cutting him. This causes those witnessing the event to think that Edward is attacking Kevin and Jim tries attacking Edward. Edward defends himself, cutting Jim’s arm before he flees to the mansion.
Kim races after Edward, while Jim obtains a handgun and follows Kim. In the mansion, Jim ambushes Edward and fights with him; Edward refuses to fight back until he sees Jim slap Kim as she attempts to intervene. Enraged, Edward stabs Jim in the stomach and pushes him from a window of the mansion, killing him. Kim confesses her love to Edward and kisses him before departing. As the police and neighbors gather, Kim tricks them by convincing them that Jim and Edward killed each other.
The elderly woman finishes telling her granddaughter the story, revealing that she is Kim and saying that she never saw Edward again. She prefers not to visit him because decades have passed and she wants him to remember her as she was in her youth. She believes Edward is still alive, immortal because he is artificial, and because of the “snow”, which Edward creates when carving ice sculptures.