With the increasing adoption of neural network models on low-resource platforms, there is a growing concern about their power consumption. Spiking Neural Networks (SNNs) have emerged as an energy-efficient promising alternative to traditional neural networks. In this paper, we propose an iterative test-generation-based approach for simplifying an SNN structure using a Satisfiability Modulo Theory (SMT) solver. The input to our framework consists of a standard SNN structure, with leaky-integrate-and-fire neurons and we output a reduced equivalent SNN with a smaller structure. The reduction is achieved by the elimination of redundant neurons identified using a test generation approach. We utilize the power of SMT solvers to carry out the simplification task. We present results on the MNIST dataset to demonstrate the utility of our method that makes SNNs better suited to low-resource platforms.