Due to the excellent comprehensive properties, Si3N4 ceramics have been widely studied and applied in the field of engineering structures. Conventional processing of Si3N4 ceramics faces a series of challenges, and laser processing has become an effective processing technology for hard and brittle materials. In this paper, a new type of dual-beam coupled nanosecond pulsed laser was used to carry out a series of ablation experiments on Si3N4 ceramic at various powers, and the laser ablation mechanism was analyzed. The equivalent diameter method and the equivalent area method were used to calculate the corresponding laser ablation threshold, and influence of laser power on surface roughness of the ablation hole edge, hole depth, removal volume and hole taper were explored. The results show that when the repetition frequency f = 10 kHz, wavelength λ = 532 nm and ablation time t = 6 s, the laser ablation thresholds of Si3N4 ceramic calculated by the equivalent diameter method and the equivalent area method are 0.55 J/cm2 and 0.59 J/cm2, respectively. In a certain power range, surface roughness of the ablation hole edge, hole depth and removal volume increase with the increase of laser power, while the ablation hole taper decreases with the increasing laser power. This innovative work is helpful to expand the scope of laser processing technology for hard and brittle materials, and has guiding significance for the optimization of laser processing technology parameters of Si3N4 ceramics.