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We report the growth of optically pumped vertical-external-cavity surface-emitting lasers (VECSELs) based on InGaSb/AlGaSb quantum wells grown on GaAs/AlGaAs distributed Bragg reflectors (DBRs). The 7.78% lattice mismatch between GaSb and GaAs is accommodated by an array of 90° misfit dislocations at the interface. This results in spontaneous relaxation of the GaSb epilayer and also significantly reduces the threading dislocation density. The VECSELs are operated in both pulsed (with 340-W peak output power) and continuous wave mode (with 0.12-W peak output power). We investigate the effects of the GaSb/GaAs interface by comparing the lattice mismatched III-Sb VECSEL grown on GaAs/AlGaAs DBRs to a lattice matched III-Sb VECSEL grown on GaSb/AlAsSb DBRs. The lattice matched VECSEL outperforms the lattice mismatched VECSEL in terms of threshold pump density, efficiency, and maximum continuous-wave output power. This can be attributed to the presence of threading dislocations throughout the active region of the mismatched VECSEL, which is confirmed by cross-sectional transmission electron microscopy. The optical properties of the III-Sb active regions are characterized by time-resolved photoluminescence, which can be used to optimize the IMF interface.