This paper presents an investigation into the use of the hydrophone as a process-monitoring sensor for the cutting of fiber-reinforced hydrogels. A sensor-rich testbed comprising of a submerged hydrophone, a load-cell and a digital camera was used to investigate the cutting of fiber-reinforced hydrogels. The mapping between the pressure and force signals reveals four distinct regions of the cutting process, viz., gel indentation, steady state gel cutting, ply indentation and ply failure. The pressure and force signals are complementary in that a positive burst pressure always corresponds to a drop in the axial thrust force. The hydrophone signal was then used as the input signal to model the time-dependent evolution of the axial thrust force, at critical regions of the cut. The hybrid modeling framework relies on region-specific modeling strategies spanning analytical, finite element method and mechanistic modeling techniques. The model was first validated using single-ply experiments and then used to predict the effect of ply-spacing in multi-ply composites. The findings show that the hydrophone is capable of providing insights into the underlying mechanics of deformation seen in soft composites, and that the hybrid modeling framework is capable of predicting the temporal evolution of the thrust force at critical regions of the cut. Overall, this work establishes the hydrophone as an effective in-situ process monitoring sensor for use during the cutting of fiber-reinforced hydrogels.