This thesis investigates the precise asymptotic behavior of the Ewens-Pitman sampling model. The Ewens-Pitman sampling model extends the classical Ewens sampling formula by incorporating both a diversity parameter and a mutation parameter, which jointly govern the distribution of partition structures. This model provides a flexible framework for studying species sampling processes, allowing for a more refined understanding of cluster growth and partition probabilities in large sample settings. Through advanced asymptotic analysis, we derive fluctuation, moderate deviation, and large deviation principles for the number of species \( K_n \) and the joint species frequency distribution \((\mathbf{M}_{n}, K_n)\). Our approach utilizes techniques such as contour deformation and the steepest descent method, resulting in precise deviation estimates and providing a systematic analysis of the joint distribution behavior of \(( \mathbf{M}_{n}, K_n)\). These findings offer new insights into the rate of convergence and the probabilities of deviations from the limiting distributions as the sample size increases. The results have significant implications for understanding the behavior of the Ewens-Pitman model in large-sample settings and pave the way for further exploration in Bayesian nonparametrics and statistical genetics.