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With advances in neural recording techniques, neuroscientists are now able to record the spiking activity of many hundreds of neurons simultaneously, and new statistical methods are needed to understand the structure of this large-scale neural population activity. Although previous work has tried to summarize neural activity within and between known populations by extracting low-dimensional latent factors, in many cases what determines a unique population may be unclear. Neurons differ in their anatomical location, but also, in their cell types and response properties. To identify populations directly related to neural activity, we develop a clustering method based on a mixture of dynamic Poisson factor analyzers (mixDPFA) model, with the number of clusters and dimension of latent factors for each cluster treated as unknown parameters. To analyze the proposed mixDPFA model, we propose a Markov chain Monte Carlo (MCMC) algorithm to efficiently sample its posterior distribution. Validating our proposed MCMC algorithm through simulations, we find that it can accurately recover the unknown parameters and the true clustering in the model, and is insensitive to the initial cluster assignments. We then apply the proposed mixDPFA model to multi-region experimental recordings, where we find that the proposed method can identify novel, reliable clusters of neurons based on their activity, and may, thus, be a useful tool for neural data analysis.