We have studied both the dynamic response and the relevant nonequilibrium dynami cal p hase transition of an Ising spin system subject to three sorts of oscillating fi eld i.e. sinusoidal, square and sawtooth waves. The above three sorts of externa l field drive dynamically the Ising spin system in either simply gradual ( abrupt) way or their combination respectively. In the case of both sinusoidal and squar e ways, it was observed that the Ising spin system displays a low_temperature sy mmetr y-breaking ordered phase and a high_temperature symmetric disordered phase as well as the dynamic transition between two dynamical phases above. We also detected the tri_critical point separating high_temperature continuous dynamic transition and low_temperature discontinuous one on the boundary of dynamic transition. The trend of dynamic transition boundary and the dependence of tri_critical point upon the system temperature, the frequency and amplitude of the driving field we re revea led as well. In contrast, nodynamic transition occurs any longer and the system always stays in symmetry-breaking ordered state if the external field takes the form of sawtooth wave. The preceding discrepancy in dynamic response and transi tion is attributed to the perturbative characteristic of different oscillating f ields.