Julie Taymor, the ousted director and co-writer of "Spider-Man: Turn Off the Dark," filed a $1 million lawsuit Tuesday against the show's producers, alleging that they are violating copyright law by using a modified version of her dialogue and stage directions.

The lawsuit, filed in U.S. District Court for the Southern District of New York, claims that the show's production company, 8 Legged Productions LLC, owes Ms. Taymor royalties for all performances since the troubled production was overhauled in April. Producers Michael...