Understanding the effects of platform motion on the performance of floating wind turbines is essential to optimize the exploitation of deep-ocean wind resources. In this work, theoretical analyses and wind tunnel experiments are conducted to study the effects of cyclic pitch motion on the power performance and wake characteristics of floating wind turbines. Theoretical analyses reveal that the rotor-available power, power variation and wake state of a floating wind turbine all depend on the Strouhal number (i.e., the normalized pitch frequency), the pitch amplitude and the pitch-radius-to-rotor-diameter ratio of the turbine (here pitch radius refers to the distance from the rotor center to the pitch rotation center). Critical Strouhal numbers are further proposed to distinguish the power performance and wake state. Power measurements show that cyclic pitch motion results in a periodic power variation. The mean power production increases with increasing pitch frequency but decreases with increasing amplitude. Both the upper and lower bounds of power variation are found to be dependent on the pitch dynamics. Wake measurements show that, for the range of pitch dynamics tested in this study, cyclic pitch motion can accelerate wake recovery and growth, depending on pitch amplitude but not on pitch frequency. Phase-averaged results suggest that the wake behavior is periodic and consequently, predictable. The cyclic pitch motion of the upstream turbine enhances its vertical wake meandering, leading to higher power production but stronger power fluctuations at downstream turbines. The propagation of periodic wake dynamics also leads to the periodicity in power outputs of downstream wind turbines.