A disk drive is disclosed comprising a first head actuated over a first disk surface and a second head actuated over a second disk surface. A first servo sector of the first disk surface is read to generate a read signal which is processed to generate a first phase error. A first clock is generated at a frequency proximate a servo data rate of the first data sector. Read signal samples are synchronized in response to the first phase error and the first clock to generate synchronous samples, and servo data in the first servo sector is detected in response to the synchronous samples. The read signal is processed to generate a second phase error, a second clock is generated in response to the second phase error, and a spiral servo track is written to the second disk surface using the second clock.