Inferring causal directions on discrete and categorical data is an important yet challenging problem. Even though the additive noise models (ANMs) approach can be adapted to the discrete data, the functional structure assumptions make it not applicable on categorical data. Inspired by the principle that the cause and mechanism are independent, various methods have been developed, leveraging independence tests such as the distance correlation measure. In this work, we take an alternative perspective and propose a subsampling-based method to test the independence between the generating schemes of the cause and that of the mechanism. Our methodology works for both discrete and categorical data and does not imply any functional model on the data, making it a more flexible approach. To demonstrate the efficacy of our methodology, we compare it with existing baselines over various synthetic data and real data experiments.