The nonlinear interaction of subcycle electromagnetic radiation with matter is the current frontier in ultrafast nonlinear optics and high-field physics. Here, we investigate nonlinear optical effects induced by intense, subcycle terahertz radiation in a doped semiconductor. We observe a truncation of the half-cycle terahertz pulse and an emission of high-frequency terahertz photons. We attribute our observations to the abrupt current drop caused by strong intervalley scattering effects. By adding an extra half-cycle terahertz pulse with opposite polarity, we monitor the evolution of the nonlinear carrier dynamics during a quasi-single-cycle pulse. Our results demonstrate the differences between nonlinear effects for subcycle and multicycle terahertz pulses. It also suggests a new approach to subcycle control of terahertz waveforms, and the generation of high-order terahertz harmonics could be realized by using multicycle pulses.