Dynamic DNA walkers can move cargoes on a surface through various mechanisms including enzymatic reactions and strand displacement. While they have demonstrated high processivity and speed, their motion dynamics are not well understood. Here, we utilize an enzyme-powered DNA walker as a model system and adopt a random walk model to provide new insight into migration dynamics. Four distinct migration modes (ballistic, Levy, self-avoiding, and diffusive motions) are identified. Each mode shows unique step time and velocity distributions, which are related to mean-squared displacement (MSD) scaling. Experimental results are in excellent agreement with the theoretical predictions. With a better understanding of the dynamics, we performed a mechanistic study, elucidating the effects of cargo types and sizes, walker sequence designs, and environmental conditions. Finally, this study provides a set of design principles for tuning the behaviors of DNA walkers. The DNA walkers from this work could serve as a versatile platform for mathematical studies and open new opportunities for bioengineering.