We propose to combine the gSlider acquisition and blip-up/down acquisition (BUDA) to achieve high-resolution and distortion-free T2 mapping. Firstly, we incorporate Hankel structured low-rank constraint into BUDA reconstruction to recover distortion-free images from blip-up/down shots without navigation. To utilize the similarity among RF-encodings and TEs, we introduce a model-based shuffling-gSlider joint reconstruction to recover high-resolution thin-slice images by gradually eliminating the weak coefficient components during the iterative reconstruction. Finally, the reconstructed images are used to obtain quantitative T2 maps. The proposed method enables distortion-free high-quality whole-brain T2 mapping with 1 mm isotropic resolution within ~1 minute.