This work presents Vision Mamba CycleGAN (VM-CycleGAN), a lightweight unpaired MRI translation framework. Existing works have focused on attention-based generators which demand high computational resources, limiting deployment in low-resource devices. Therefore, VM-CycleGAN has been proposed by introducing a Vision Mamba-based generator, leveraging state-space modeling that requires lower computational complexity without compromising system performance. In this work, a dual-generator adversarial setup has been implemented and trained considering multiple losses particularly texture and structural loss to preserve visual and anatomical fidelity. For validation, benchmark UNC 3T-7T dataset has been taken into account. For experiment, a combination of the three individual anatomical planes of T1w and T2w volumes has been used. Results and analysis show that proposed method achieves a peak PSNR of 32.63 and SSIM of 0.90 which is very consistent. Further, VM-CycleGAN reduces parameters by 58% and FLOPs by 62% compared to an attention-based baseline. Results confirm its high-fidelity synthesis and efficiency, making it suitable for deployment in resource-constrained clinical environments.