Mid-infrared (MIR) femtosecond lasers, resonant with the absorption bands of amide-related molecular groups in the range of 6.1 to 6.5 μm, have been demonstrated to be effective for tissue ablation. However, the flexible and stable delivery of such pulses to micrometer-scale tissue regions for controlled ablation remains challenging. Here, we utilize a silica-based anti-resonant hollow-core fiber (AR-HCF) to deliver high-power MIR femtosecond pulses with high temporal and spectral fidelity, featuring pulse durations of approximately 340 fs and peak power densities exceeding 1 GW/cm², for selective tissue ablation. Benefiting from the small numerical aperture of the AR-HCF, a relatively stable and consistent beam spot size can be maintained over a millimeter-scale propagation distance. Precise control of the ablation depth can be achieved by appropriately selecting the scanning parameters, with penetration depths reaching the sub-millimeter scale. Furthermore, for the first time, we systematically compare the tissue ablation performance of MIR femtosecond lasers at resonant wavelengths (6.4 and 6.1 μm) and a non-resonant wavelength (5.5 μm) under identical scanning conditions. An ablation depth ratio of more than 8:1 is observed, demonstrating the high efficiency and selectivity of the resonance-based ablation mechanism. These results establish flexible delivery of high-power MIR femtosecond pulses in tissue-resonant bands via silica-based AR-HCF as a powerful platform for selective, precise, and efficient tissue ablation, providing a promising approach for interventional and minimally invasive surgery.