We have developed a method using measurements on drill cuttings as well as calibrated models to estimate anisotropic mechanical properties and stresses in unconventional reservoirs, when logs are not available in lateral wells. We measured mineralogy and organic matter on cuttings using diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). We described the methodology and illustrated it using two vertical control wells in the Vaca Muerta Formation, Argentina, and one lateral well drilled in the low-maturity oil-bearing reservoir. The method has two steps. First, using a vertical control well containing measurements from cuttings, a comprehensive logging suite, cores, and in situ stress tests, we define and calibrate four models: petrophysical, rock physics, dynamic-static elastic, and geomechanical. The petrophysical model provides petrophysical constituent volumes (mineralogy, organic matter, and fluids) from logs or DRIFTS inputs to the rock-physics model for calculating the dynamic anisotropic elastic moduli. The dynamic-static elastic and geomechanics models provide the relationships for computing static elastic properties and the minimum stress. Second, we acquire DRIFTS data on cuttings in the target lateral well and apply the four models for calculating stresses. We find that the method is successful for two reasons. First, the sonic-log-derived elastic moduli could be reconstructed accurately from the rock-physics model using input from petrophysical volumes from logs and DRIFTS data. A striking observation is that the elastic-property heterogeneity in those wells is explainable almost solely by compositional variations. Second, petrophysical volumes can be reconstructed by the petrophysical model and DRIFTS data. In the lateral well, we observed horizontal variations of mineralogy and organic matter, which controlled variations of elastic moduli and its anisotropy, and, in turn, affected partitioning of the gravitational and tectonic components in the minimum stress. This methodology promises accurate in situ stress estimates using cutting-based measurements and assessments of unconventional-reservoir heterogeneity.