Polarization manipulation is a significant issue for artificial modulation of the electromagnetic (EM) wave, but general mechanisms all suffer the restriction of inherent symmetric properties between opposite handedness. Herein, a strategy to independently and arbitrarily manipulate the EM wave with orthogonal circular polarizations based on a metasurface is proposed, which effectually breaks through traditional symmetrical characteristics between orthogonal handedness. By synthesizing the propagation phase and geometric phase, the appropriate Jones matrix is calculated to obtain independent wavefront manipulation of EM waves with opposite circular polarizations. Two transmissive ultra-thin meta-deflectors are proposed to demonstrate the asymmetrical refraction of transmitted circularly polarized waves in the microwave region. Simulated transmitted phase front and measured far-field intensity distributions are in excellent agreement, indicating that the transmitted wave with different polarizations can be refracted into arbitrary and independent directions within a wide frequency band (relative bandwidth of 25%). The results presented in this paper provide more freedom for the manipulation of EM waves, and motivate the realizations of various polarization-independent properties for all frequency spectra.