In high contrast to traditional geometric meta-surfaces, which can only operate on the cross-polarized field, we propose a bi-functional meta-device with full energy utilization in both co- and cross-polarized fields. In this paper, co-polarized refraction and cross-polarized focusing are integrated in one single meta-surface by taking advantage of compound propagation and geometric phases. A multi-layer element structure with various geometric degrees of freedom is designed to realize simultaneous and independent phase modulation of both co- and cross-polarized transmitted waves. The derived criterion is verified in the microwave region, and the proof-of-concept experiments indicate that the proposed meta-surface can have distinct functionalities with orthogonal polarizations in the transmitted field with a specific circularly polarized illumination. This scheme for bi-functional meta-surface construction provides an effective method to manipulate both co- and cross-polarized output fields simultaneously, which can extremely enhance the modulation efficiency of output energy. Different output wavefronts can be conveniently switched by filtering only the polarization state of the output end, simplifying the operational complexity of the bi-functional meta-system. This criterion paves the way for flexible manipulation of electromagnetic waves with a higher degree of freedom and facilitates a larger diversity of applications across the whole frequency spectrum.