We theoretically investigate the modulation efficiency, response time, and pump power of a terahertz-beam intensity modulator by using an organic photonic crystal slab structure with high quality factor "defect" cavity. The basic operation of an ultrafast low-power terahertz wave modulator actuated by the dynamical shifts of the defect mode induced by pump intensity is discussed in detail. The finite-difference time-domain method is used to verify and analyze the characteristics of the terahertz wave modulator. The device exhibited extinction ratio of 47.15 dB and insertion loss of 3.2 dB at frequency of 1.062 THz with ultrafast response times on the order of several picoseconds.