We present results from observations of the magnetar 1E 1547.0-5408 (SGR J1550-5418) taken with the Chandra X-ray Observatory and the Rossi X-ray Timing Explorer (RXTE) following the source's outbursts in 2008 October and 2009 January. During the time span of the Chandra observations, which covers days 4 through 23 and days 2 through 16 after the 2008 and 2009 events, respectively, the source spectral shape remained stable, while the pulsar's spin-down rate in the same span in 2008 increased by a factor of 2.2 as measured by RXTE. The lack of spectral variation suggests decoupling between magnetar spin-down and radiative changes, hence between the spin-down-inferred magnetic field strength and that inferred spectrally. We also found a strong anti-correlation between the phase-averaged flux and the pulsed fraction in the 2008 and 2009 Chandra data, but not in the pre-2008 measurements. We discuss these results in the context of the magnetar model. ; Comment: 4 figures, accepted for publication in ApJ