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In this paper, we develop a spatiotemporal mathematical model for analyzing the performance of prioritized data transmissions in the device-to-device (D2D) underlaying cellular network. A dynamic interference model of a D2D user is constructed by exploiting thinned Poisson point process to model the D2D user location with data stored in the buffer. A dynamic priority queuing model is adapted to analyze the performance of multiple types of traffic, in which the priority jump strategy is proposed to provide increased transmission opportunity for low-priority user packets. Then, we employ a two-dimensional Geo/G/1 Markov chain to describe a queue model with priority jump and evaluate it using quasi-birth-and-death process approach. An iterative solution is used to compute the steady-state probability distribution and the expressions of performance metrics are obtained. The simulation results show the validity of the theoretical analysis. Moreover, by comparing the dropping probability of the priority queuing model with and without the jump strategy, the rationality of the introduced model is confirmed.