Three missing data processing methods, namely zero padding, linear model fitting, and resampling, were proposed to evaluate the frequency stability of atomic clocks in presence of data interruption and date gap. A direct calculation method for calculating overlapping Hadamard variance was also proposed. Based on clock error simulation data, the influence of different processing methods on frequency stability calculation was compared and analyzed. The results show that when the data missing rates are below 1%, 10%, and 20%, the stability calculated by zero padding, linear model fitting, and resampling methods is relatively close to the true stability. Zero padding and linear model fitting methods are only suitable for situations with less missing data, while resampling methods have better applicability than the first two methods. Furthermore, the direct calculation method can accurately evaluate stability even when the data missing rate reaches 50%. In cases where there is a large amount of missing data, the original data can be directly used for stability evaluation. Finally, the frequency stability of the BDS-3 on-board clock with missing clock bias data was evaluated. It is shown that the stability of the rubidium clock and hydrogen clock were better than 2.12×10^-14 and 2.15×10^-15 at the sampling time of 10 000 seconds and one day, respectively, and was generally at the same level as GPS Ⅲ A rubidium clocks and Galileo hydrogen clocks.