The Torah says, “They stripped him of his tunic, the fine woolen tunic that was on him.”
Rashi comments on the obvious superfluous words. He says they stripped him of the special coat that his father made for him, and they also stripped him of his regular clothes that he wore under the special coat.
They claimed that they were jealous of him because of the extra special treatment that Yosef was given by their father. If that was the case, they could have just stripped him of his special coat, and that would have made things fair.
But their jealousy was greater than that. They hated him, and they didn’t just want to see things fair, they wanted Yosef to be lower than they were. They stripped him completely naked, revealing that they were not out for justice, they were out to completely humiliate and destroy Yosef.
Just like the story where Solomon offered to split the baby. You could tell the real mother because she was interested in the welfare of the child. The one who claimed to be the mother only wanted to see the other woman be as miserable as she was.