With the increasing demand for high spectral efficiency(>10 bps/Hz) and ultra?reliability (BER(Bit Error Rate)<10??) in 6G communications, this paper proposes a joint Orthogonal Time Frequency Space(OTFS) waveform design for terahertz(THz)?based Low?Earth Orbit(LEO) satellite communications. Aiming at challenges including 1.2 MHz Doppler shifts,120 μs delay spreads, and power amplifier nonlinearity(requiring PAR(Peak?to?Average Ratio)<4 dB) in satellite-terrestrial links, a Fractional Fourier Transform(FrFT)?based super?resolution channel estimation(error≤3 kHz) is developed,an Intelligent Reflecting Surface(IRS)?assisted 3D spatio-temporal-frequency beamforming architecture with 256 elements is established, and a Riemannian manifold?constrained constant envelope precoding algorithm is designed. Simulation results demonstrate that at 0.3 THz with 7 km/s relative velocity, the system achieves a BER of 1×10^-7, a PAR of 3.5 dB, and a spectral efficiency of 12.4 bps/Hz(40% improvement over Orthogonal Frequency Division Multiplexing(OFDM)), while boosting power amplifier efficiency from 12.7% to 78.4%. Validated by 3rd Generation Partnership Project(3GPP) Non-Terrestrial Network(NTN) channel models, this scheme provides a highly robust and power-efficient waveform solution for 6G space-terrestrial integrated communications.