The scissors are a phallic symbol in the narrative. Elisa's association with the scissors helps illustrate how power works between men and women within the arc of the story. When the reader first meets Elisa, she is described as both "lean and strong" and "blocked and heavy." Several lines afterwards, the scissors she uses are described as "short and powerful," a description which is similar both to Elisa's figure. Elisa's physicality appears male--she is not described with the curves of a woman, but rather the square figure of a man. Her use of the phallic scissors increases the association. She even wears men's clothing while she gardens. The garden is where she is most powerful. The fertile garden is a symbolic womb, and yielding the symbolic phallus means that Elisa is both man and woman in this world--she doesn't have to wait for a man to help her, she can do it on her own.
The scissors continue to be a source of power in Elisa's encounters with the tinkerer. He offers to sharpen her scissors--which feels sexual in nature--and she assures him that she can sharpen her own scissors. Finally, Elisa allows him to fix the hole in her pot--another seemingly sexual situation--although it is made clear to the reader that this is out of pity, not out of necessity. Her charged interactions with the tinkerer show the reader that she can take care of herself.
However, the scissors disappear at the end of the story. With the powerful symbol gone, so to does Elisa's power dissipate. Her husband recognizes her strength--is surprised by it, even--but it is gone by the end of the story. After she realizes the tinkerer threw away her chrysanthemums--which she tended to so carefully with her scissors--she realizes her own weakness, and her strength is gone.