Manipulation of terahertz (THz) wave plays an important role in THz imaging, communication, and detection. The difficulty in manipulating the THz wave includes single function, untunable, and inconvenient integration. Here, we present a mechanically tunable THz polarizer by using stretchable buckled carbon nanotube sheets on natural rubber substrate (BCNTS/rubber). The transmittance and degree of polarization of THz wave can be modulated by stretching the BCNTS/rubber. The experiments showed that the degree of polarization increased from 17% to 97%, and the modulation depth reached 365% in the range of 0.2-1.2 THz, as the BCNTS/rubber was stretched from 0% to 150% strain. These changes can be also used for high strain sensing up to 150% strain, with a maximum sensitivity of 2.5 M/S. A spatial modulation of THz imaging was also realized by stretching and rotating BCNTS/rubber. The theoretical analysis and numerical modeling further confirm the BCNTS/rubber changes from weak anisotropic to highly anisotropic structure, which play key roles in THz wave modulation. This approach for active THz wave manipulation can be widely used in polarization imaging, wearable material for security, and highly sensitive strain sensing.