In contemporary biomedical research, microscopic image segmentation has emerged as an indispensable analytical task. However, complex morphologies and diverse sizes of cellular structures make accurate cell segmentation challenging. Although deep learning based methods have shown great potential in microscopic image segmentation, they come with high computational complexity, reliance on extensive GPU resources, large parameter counts, and high power consumption. To address these challenges, this paper introduces a novel, computationally efficient framework that integrates the Mamba with Spiking Neural Networks (SNNs) for biomedical applications. Spiking MU-Net maintains accuracy comparable to state-of-the-art methods while significantly reducing computational load, parameter size, and power consumption. Specifically, (1) We propose a spiking neuron-based model that integrates Mamba and convolutional modules, enabling discrete, addition-only operations. This design significantly reduces computational overhead and parameter count, paving the way for real-time microscopy analysis. (2) Experiments on multiple cell datasets demonstrated that our method achieved high accuracy with a DSC of 83% while significantly reducing energy consumption to just 3.22mJ. (3) Our approach attained accuracy comparable to ANN-based networks, with a DSC improvement of 1.04%, while achieving the lowest energy consumption among SNN-based segmentation models, reducing parameters by 10.21M and energy by 0.29mJ.