In this work, a high-efficiency full-space metasurface (MS) is demonstrated numerically, which can independently manipulate the transmitted linear polarization (LP) and the reflected circular polarization (CP) wavefront based on the transmission and geometric phase at terahertz (THz) range. The unit-cell of the full-space MS is composed of a C-shaped slot structure sandwiched with two twisted outer single-split-rings (SSRs) and parallel inner double-split-rings (DSRs). The proposed MS structure can achieve cross-polarization conversion of LP waves after transmission at the lower frequency (f1=0.55 THz), and CP waves after reflection at the higher frequency (f2=1.37 THz). The full 2π phase shifts of the transmitted cross-polarization wave and reflected orthogonal CP wave can be obtained independently by adjusting the opening direction and size of the C-shaped slot structure based on the transmission phase, and the orientation angle of the parallel inner DSRs structure based on geometric phase, respectively. In particular, anomalous refraction and reflection for LP and CP wave, focusing lens and vortex beam generation are also demonstrated numerically. These findings are beneficial in expanding the scope of full-space MS for wavefront manipulations, providing new possibilities to develop multifunctional THz device for both LP and CP waves.