The train schedule and timing don't tell the full story. Typically, people want to visit the upper portion of Taormina not the train station, which is at the bottom of the hill. A taxi would be required back and forth from/to the train station to enjoy the sights and get back to Siracusa. Really, this is not a good candidate for a DIY excursion.
Oh yes.... don't forget about travelling back and forth to the Siracusa rail station.