The response of Damask rose to drought and the underlying mechanisms involved are not known. In this study, vegetative, propagated rose plants were grown under control and water-deficit conditions in a greenhouse at Taïf University, south-west of Saudi Arabia. Control plants were irrigated to field capacity (FC), while water-stressed plants were irrigated to either 50% FC (mild stress) or 25% FC (severe stress). After 60 days, leaf, stem and root fresh and dry weights (g plant−1), photosynthetic activity, leaf water potential (Ψw), leaf water content (WC), apoplastic water fraction (AWF), osmotic potential at full turgor (Ψs100) and turgor loss point (Ψs0), cell wall elasticity, osmotic adjustment (OA), and some solutes (K+, Ca2+, Cl−, proline and soluble carbohydrates) were evaluated. Water stress significantly decreased fresh and dry weights of R. damascena and all photosynthetic parameters, apart from leaf temperature, which increased. Severe water stress (25% FC) resulted in more negative Ψs100 and Ψs0 values than the mild water stress and control. The AWF did not significantly change in response to water stress. The leaf bulk modulus of elasticity (ε) increased from 2.5 MPa under well-watered conditions to 2.82 and 3.5 MPa under mild and severe water stress, respectively. R. damascena experienced OA in response to water stress, which was due to the active accumulation of soluble carbohydrates and, to a lesser degree, proline under mild stress, along with tissue dehydration (passive OA) under severe stress. Overall, we identified two important mechanisms of drought tolerance in R. damascena—osmotic and elastic adjustment—but they could not offer resistance to water stress beyond 25% FC.