Token merging (ToMe) reduces the computational cost of Vision Transformers (ViTs) by merging similar tokens. However, ToMe may inadvertently merge critical tokens, leading to accuracy degradation. Furthermore, the sequential execution of ViT and ToMe operations incurs increased latency on edge GPUs. To address these challenges, we propose TiMM, a token-importance-aware merging method that preserves essential tokens by considering both token importance and similarity. We also present a dedicated FPGA-based accelerator designed to exploit the concurrent execution between ViT and TiMM. Experimental results across DeiT-Tiny, Small, and Base demonstrate that TiMM achieves accuracy improvements of 0.23%-0.73% over ToMe, respectively, within a 1% accuracy drop margin relative to the baseline. When implemented on the Xilinx ZCU102, it demonstrates speedups of 1.45×-10×, along with energy efficiency gains of 1.03×-3.1× compared to the NVIDIA Jetson TX2.