Light-metal hydrides, like MgH2, remain under scrutiny as prototypes for reversible H-storage materials. For MgH2, we assess hydrogen desorption/adsorption properties (enthalpy and kinetic barriers) for stepped, catalyst-doped surfaces occurring, e.g., from ball-milling in real samples. Employing density functional theory and simulated annealing in a slab model, we studied initial H2 desorption from stepped surfaces with(out) titanium (Ti) catalytic dopant. Extensive simulated annealing studies were performed to find the dopant’s site preferences. For the most stable initial and final (possibly magnetic) states, nudged elastic band (NEB) calculations were performed to determine the H2-desorption activation energy. We used a moment-transition NEB method to account for the dopant’s transition to the lowest-energy magnetic state at each image along the band. We identify a dopant-related surface-desorption mechanism that reloads via bulk H diffusion. While reproducing the observed bulk enthalpy of desorption, we find a decrease of 0.24 eV (a 14% reduction) in the activation energy on doped stepped surface; together with a 22% reduction on a doped flat surface, this brackets the assessed 18% reduction in kinetic barrier for ball-milled MgH2 samples with low concentration of Ti from experiment.