<p>A novel rate-dependent cohesive phase-field model is proposed that can simulate dynamic mixed-mode hydraulic fractures. Compared with the quasistatic model, the proposed model considers the contributions of the kinetic energy of crack propagation and phase-field evolution damping to dynamic fracture. The crack driving force is decomposed into tensile, compressive and tensile/compressive‒shear parts, but only the tensile and tensile‒shear parts drive the propagation of mode I and mode II fractures, respectively. The critical energy release rate calculation for mixed-mode fractures is based on the Benzeggagh–Kenane semiempirical damage criterion, which achieves a continuous transition from mode I to mode II fractures without segmentation compared with the other criteria. The traction–separation law with linear softening is used to capture the quasi-brittle fracture behavior of rock materials. The fracture permeability is derived according to the Reynolds lubrication equation, and a quadratic transition function is used to relate it to the matrix permeability. The phase-field evolution equation and the stress balance equation are derived via the Francfort–Marigo variational principle, and then, the proposed model is spatially discretized via the multifield finite element method and numerically solved via the staggered algorithm. The accuracy and applicability of the proposed model in terms of dynamic fracture and mixed-mode fracture are verified by benchmark tests of dynamic fracture and tensile‒shear mixed-mode fracture, respectively. Finally, the propagation patterns and fluid pressure responses of dynamic hydraulic fractures in homogeneous and fractured reservoirs are investigated.</p>