Injection-induced seismicity has become one of the most critical challenges for the widespread deployment of Enhanced Geothermal Systems (EGS). In particular, some EGS development projects have led to large, damaging earthquakes that unexpectedly occurred far off the stimulated reservoir region and, in particular, after stopping fluid injection. Yet, the causative mechanisms of these seismicity patterns remain highly elusive. Here, we identify a combination of mechanisms that could explain delayed seismicity in EGS sites by conducting fully-coupled hydromechanical simulations of the hydraulic stimulation of a naturally-fractured granitic reservoir. The model comprises a sparse network of long, variably-oriented fractures interacting with a nearby, critically-oriented fault. The results show that the presence of fractures introduces notable nonlinearities in the flow field and rock deformation and significantly expands the rock volume affected by fluid injection. First, the stimulated fracture network provides highly-permeable conduits for communicating elevated pore pressure over long distances. Second, the anisotropic expansion of fractures generates shear stress that is transmitted almost instantaneously across the reservoir. The pore pressure and stress perturbations can not only cause slip along fractures, inducing (micro)seismicity during injection, but also affect the stability of nearby faults, which may not necessarily be pressurized during injection. The transferred poroelastic stresses can increase or decrease the slip tendency along different fault segments. However, the fault may reactivate only after several months following injection when a progressive pore pressure diffusion modulated by the transient fault permeability evolution brings a critically-stressed fault segment to failure conditions. We also find that the spatiotemporal evolution of seismicity depends largely on the nearby fault orientation, hydromechanical properties, and hydraulic connection with the fracture network, as well as the initial state of stress. We conclude that accurate subsurface characterization and continuous monitoring during and after injection should allow for managing the risks posed by injection-induced seismicity and safely unlocking the immense potential for clean and sustainable geothermal energy.