Differential privacy provides a principled framework for protecting sensitive data, yet existing private hypothesis testing methods often suffer from impracticality or significant power loss. We propose a general framework for differentially private permutation tests that extends classical non-private permutation tests while strictly preserving finite-sample validity. We characterize conditions for consistency and non-asymptotic uniform power, highlighting the role of the test statistic. As a concrete instantiation, we develop differentially private kernel tests for two-sample and independence testing. These methods are simple to implement, applicable to diverse data types, and achieve minimax-optimal power across privacy regimes.