We present a broadband spectral-timing analysis of SMC X-1 at different intensity states of its superorbital variation using 10 Suzaku and 6 Nuclear Spectroscopic Telescope Array (NuSTAR) observations. The spectrum in all the states can be described by an absorbed power law with a high-energy cutoff and a blackbody component along with an iron emission line. Compared to other supergiant high-mass X-ray binaries, the Fe Kα line equivalent width is low in SMC X-1—from less than 10 eV in the high state to up to ∼270 eV in the low states. The spectral shape is dependent on flux, with the hard X-ray spectrum steepening with increasing flux. We also report a highly variable normalization of the power-law component across these 16 superorbital states. Pulsations in the hard X-rays for both the instruments were detected in all but two observations. The pulse profiles are near sinusoidal, with two peaks and the relative intensity of the second peak decreasing with decreasing luminosity. These findings suggest that the superorbital modulation in SMC X-1 is not caused by absorption in precessing warped accretion disk alone and there are intrinsic changes in X-rays emanating from the neutron star at different superorbital states. We also note a putative cyclotron line at ∼50 keV in the NuSTAR spectra of three bright states, indicating a possible magnetic field of ∼4.2 × 1012 G. Finally, with the new pulse period measurements reported here, the time base for the secular spin-up of SMC X-1 is increased by thirteen years and the complete pulse period history shows a sudden change in the spin-up trend around 1995.