Optimizing computing circuits such as multipliers and adders is a fundamental challenge in modern integrated circuit design. Recent efforts propose formulating this optimization problem as a reinforcement learning (RL) proxy task, offering a promising approach to search high-speed and area-efficient circuit design solutions. However, we show that the RL-based formulation (proxy task) converges to a local optimal design solution (original task) due to the deceptive reward signals and incrementally localized actions in the RL-based formulation. To address this challenge, we propose a novel model-based circuit genetic evolution (MUTE) framework, which reformulates the problem as a genetic evolution process by proposing a grid-based genetic representation of design solutions. This novel formulation avoids misleading rewards by evaluating and improving generated solutions using the true objective value rather than proxy rewards. To promote globally diverse exploration, MUTE proposes a multi-granularity genetic crossover operator that recombines design substructures at varying column ranges between two grid-based genetic solutions. To the best of our knowledge, MUTE is the first to reformulate the problem as a circuit genetic evolution process, which enables effectively searching for global optimal design solutions. We evaluate MUTE on several fundamental computing circuits, including multipliers, adders, and multiply-accumulate circuits. Experiments on these circuits demonstrate that MUTE significantly Pareto-dominates state-of-the-art approaches in terms of both area and delay. Moreover, experiments demonstrate that circuits designed by MUTE well generalize to large-scale computation-intensive circuits as well.