In this work, we present an optimization framework aimed at reducing the sampling overhead associated with circuit cutting in quantum computing. We design a complete pipeline that integrates circuit rewriting, overhead evaluation via qiskit-addon-cutting, and heuristic search using simulated annealing and genetic algorithms. To enable more efficient circuit representations, we propose six rewriting techniques, including methods that exploit gate commutativity and ZX-Calculusbased transformations. The latter allows flexible rewrites through diagrammatic rules such as simplification, local complementation, and pivoting. Our experimental evaluation on benchmark circuits demonstrates that ZX-based strategies significantly reduce sampling overhead, while pure commutativity-based approaches show limited gains. To improve scalability, we introduce a windowed rewriting approach that targets random circuit sections, offering further performance benefits. Comparative results reveal that simulated annealing consistently finds lower-overhead solutions, whereas the genetic algorithm provides superior runtime performance through parallel evaluation. Our findings highlight the value of structured rewriting and search-based optimization in preparing circuits for circuit cutting.