Metasurfaces have attracted tremendous attention due to their outstanding performance in manipulating electromagnetic waves. However, the intrinsic dispersion and lack of tunability impose a severe restriction on applications like optical switch and compact beam deflectors. Besides, conventional achromatic metadevices sizes based on aperiodic configurations are relatively small due to the limited phase dispersion control range. Here, we propose a quasi-2π phase coverage approach to construct a periodic and reconfigurable metasurface that is capable of realizing achromatic and dynamic switching between two deflections in the microwave with infinitely large size. With delicate arrangement of polarization-independent meta-atoms and the selective stimuli of varactor diodes, broadband response and flexible tunability, two contradictory characteristics of conventional resonant meta-atoms, can be accordingly fulfilled with our method. The relative bandwidth of achromatic deflection can reach 46.7% and the switching of deflection directions can be achieved through adjusting the bias voltage. This reconfigurable metasurface paves the way for dispersion-free and switchable manipulations of electromagnetic waves that may lead to advances in a variety of applications, such as wireless power transfer and information processing.