Emerging internet‐of‐things technologies require widespread antennas and sensors. They should be cheap enough to be widely deployed, but still should be highly functional and tunable. Here, a thorough, in‐depth study of spectral shifts and phase vortices in kirigami Fano‐resonant metamaterials is presented. Microwave metamaterials are printed on paper using metal inks. Then, the printed metamaterials are cut line‐by‐line and folded, so that a step height between neighboring unit cells can be created. By varying step heights, significant spectral tuning as well as resonance switching are obtained. The large spectral shift of the highly asymmetric Fano lineshape also enables significant control of radiation direction. The observations are explained based on the interactions between neighboring unit cells. Moreover, phase singularities are found at the zero‐amplitude position of the Fano resonance spectrum, and a pair of phase vortices appear in parameter space. The kirigami metamaterials allow an easy parameter scan, and therefore significant control of the spectral phase becomes possible. Such drastic phase changes around singularity points could be very useful for various applications, including optical sensing and wavefront manipulation. The kirigami metamaterials enable easily fabricated but highly functional and tunable elements, which could be useful for various antennas and sensors.