We develop a new coupled hydro-mechanical-chemical (HMC) model to investigate the stress-controlled evolution of dissolution cavities along a hectometer-scale heterogeneous fracture. The fracture is conceptualized to consist of numerous patches associated with spatially-variable, stress and dissolution-dependent local stiffnesses and apertures. We consider the complete coupling relationships among mechanical deformation, fluid flow, and chemical dissolution within the fracture. More specifically, our model captures non-linear fracture deformational responses and their consequences on localized flow pattern and dissolutional aperture growth, as well as the feedback of dissolution to mechanical weakening and stress redistribution. We elucidate how geomechanical processes affect the aperture and flow patterns and the formation of small to large dissolution cavities. Our simulation results show that stress retards the permeability increase with the extent of retardation positively related to a dimensionless penetration length l_p′. Stress induces the splitting of the dissolution front, promoting localized flow and branched dissolution. At low l_p′ (wormhole dissolution regime), stress also promotes the sustained growth of dissolution branches. Hence, there is no apparent increase in global flow heterogeneity. At high l_p′, stress transitions the system from uniform dissolution into wormhole formation. Wormholes initiate from remote stiffer regions and converge toward the inlet. Our results have important implications for understanding various dissolution phenomena in subsurface fractured rocks, ranging from karstification to reservoir acidization.