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Numerous studies have reported the occurrence of aseismic slip or slow slip events along faults induced by fluid injection. However, the underlying physical mechanism and its impact on induced seismicity remain unclear. In this study, we develop a numerical model that incorporates fluid injection on a fault governed by rate‐and‐state friction to simulate the coupled processes of pore‐pressure diffusion, aseismic slip, and dynamic rupture. We establish a field‐scale model to emulate the source characteristics of induced seismicity near the Dallas‐Fort Worth Airport (DFWA), Texas, where events with lower‐stress drops have been observed. Our numerical calculations reveal that the diffusion of fluid pressure modifies fault criticality and induces aseismic slip with lower stress drop values (<1 MPa), which further influence the timing and source properties of subsequent seismic ruptures. We observe that the level of pore‐pressure perturbation exhibits a positive correlation with aseismic‐stress drops but a reversed trend with seismic‐stress drops. Simulations encompassing diverse injection operations and fault frictional parameters generate a wide spectrum of slip modes, with the scaling relationship of moment (M0) with ruptured radius (r0) following an unusual trend, M0∝r04.4 ${M}_{0}\propto {r}_{0}^{4.4}$, similar to M0∝r04.7 ${M}_{0}\propto {r}_{0}^{4.7}$ observed in the DFWA sequence. Based on the consistent scaling, we hypothesize that the lower‐stress‐drop events in the DFWA may imply less dynamic ruptures in the transition from aseismic to seismic slip, located in the middle of the broad slip spectrum, as illustrated in our simulations. Plain Language Summary: Injection‐induced earthquakes have presented significant obstacles to developing energy resources related to fluid injection, such as enhanced geothermal systems and shale gas development. Despite their prevalence, the causes and impact of these earthquakes are not fully understood. Aseismic slip, characterized by slower velocities and longer durations than typical earthquakes, has been observed in induced earthquake studies. In this study, we use a numerical model to investigate how fluid pressures influence the slip properties of induced seismicity near the Dallas‐Fort Worth airport (DFWA), Texas. Our model shows that elevated fluid pressure induces aseismic slip and advances or delays fast slip (i.e., earthquakes). The pore‐pressure perturbation alters the source characteristics of both aseismic‐slip events and seismic ruptures, enhancing aseismic‐stress release while diminishing seismic‐stress release. Simulations involving various fault frictional properties reveal a wide spectrum of slip modes, ranging from slow to rapid slip, which are different from the stress‐release processes that drive globally observed natural earthquakes, but exhibit similarities to observations in the DFWA. Consequently, we infer that the DFWA events may exhibit reduced dynamic characteristics akin to slow slip events positioned in the middle of the broad spectrum generated in our modeling. Key Points: Pore‐pressure change induces aseismic slip with lower stress drops, either advancing or delaying seismic rupturesPore‐pressure perturbation exhibits a positive correlation with aseismic‐stress drops but a reversed trend with seismic‐stress dropsSimulations show a wide spectrum of induced‐slip behavior, exhibiting a similar source scaling to observations [ABSTRACT FROM AUTHOR]