A class of anisotropic, transmissive electromagnetic metasurfaces is presented, which enable independent and simultaneous control of copolarized phase and amplitude responses to two linear, orthogonal polarizations. By varying the geometrical parameters, the transmission response of the proposed structure can yield a full phase coverage, accompanied by broadly adjustable amplitude and negligible cross-polarized components. The full amplitude-phase control together with the novel anisotropic character allows efficient implementation of complicated field manipulations. As representative application examples, which cannot be realized via conventional (phase-only) metasurfaces, it is presented here: (1) the radiation of multiple equal-power vortex beams (along arbitrarily predesigned directions, with designable orbital angular momentum modes under different polarizations), and (2) the realization of polarization-reconfigurable multifocal metalenses. Full-wave numerical simulations and experimental results demonstrate good agreement and confirm the versatility and effectiveness of the proposed approach to design advanced field-manipulation systems.