Dust polarization depends on mechanical properties of dust as well as on local environments. To understand how dust polarization varies with different properties, we model the wavelength-dependence polarization of starlight and polarized dust emission of aligned grains by simultaneously taking into account grain alignment and rotational disruption by radiative torques (RATs). We explore a wide range of the local radiation field and grain mechanical properties characterized by tensile strength (Smax). We find that the peak wavelength shifts to shorter wavelengths as the radiation strength (U) increases due to the enhanced alignment of small grains. Grain rotational disruption by RATs tends to decrease the optical-NIR polarization but increase the UV polarization of starlight due to the conversion of large grains into smaller ones. In particular, we find that the polarization degree at 850 μm (P850) does not increase monotonically with U or grain temperature (Td), but it depends on Smax of the grains. Our model can be tested with observations toward star-forming regions or molecular clouds irradiated by a nearby star, which have higher radiation intensities than the that of the average interstellar radiation field. Finally, we compare our predictions of the P850-Td relationship with Planck data and find that the observed decrease of P850 with Td can be explained when grain disruption by RATs is accounted for, suggesting that as interstellar grains are unlikely to have a compact structure, perhaps they have a composite one. The variation of the polarization degree with U (or Td) can provide a valuable constraint on the internal structure of cosmic dust.