Climate change scenarios and water restrictions are key challenges for Mediterranean citriculture, requiring sustainable deficit irrigation (DI) strategies to ensure sustainable yields. Further research on the physiological pathways that regulate crop responses to water stress is necessary. This work describes the physiological limitations induced under drought conditions in young Navelina orange trees, including the crop’s capability to recuperate its physiological status upon rewatering and after water withholding. A trial was conducted in two-year-old trees subjected to three irrigation treatments: a full irrigation treatment (FI) and two different DI strategies. The results show significant decreases in gas exchange rates for stem water potential (ΨStem) values below −1.5 MPa, evidencing diffusive limitations from drought stress. Additionally, there was evidence of increased osmolyte synthesis, a preventative response to oxidative damage. Significantly increased levels of proline (Pro) and malondialdehyde (MDA) were observed with higher levels of water stress (ΨStem < −1.8 MPa), which leads us to assume that this threshold signals the presence of oxidative damage with no capacity for subsequent recovery, probably affecting the final yield.