In this paper, we propose a Hierarchical Adaptation framework for Slide-level Domain-shift (HASD), a slide-level domain adaptation framework, to address the domain-shift problem of pathology data, which is heavily influenced by center-specific conditions in pathology AI. HASD integrates domain-level alignment solver, slide-level geometric invariance regularization, and patch-level attention consistency regularization to achieve multi-scale feature consistency and perform computationally efficient slide-level domain adaptation. It also reduces the computational overhead through a prototype selection mechanism. On two slide-level tasks across five datasets, we achieve 4.1% AUROC improvement in a breast cancer HER2 grade cohort and 3.9% C-index improvement in a UCEC survival prediction cohort, providing a practical and reliable slide-level domain adaptation solution.