Water deficit and increasing pressure on water resources in semi-arid regions has led to the spread of irrigation with non-conventional water resources, such as desalinated seawater (DSW). The few existent studies to date, mainly carried out in Israel and Spain, have shown that suitable management of irrigation with DSW must be performed to avoid agronomic problems and reductions in crop productivity and fruit quality in the mid-long term. To the best of our knowledge, in the case of citrus, fruit production, and quality, information on the effects of DSW irrigation is not available. In this study, we evaluated the short-term agronomic and economic effects of irrigating a mandarin orchard during two crop cycles (2017–2019) with (i) fresh water (FW), (ii) desalinated seawater (DSW), and (iii) a mix of water composed of 50% FW and 50% DSW. Stem water potential (Ψs < −1 MPa) and gas exchange parameters (net photosynthesis; A > 6.5 µmol/m2/s and stomatal conductance; gs > 65 mmol/m2/s) indicated that trees were well irrigated throughout the experiment. The concentration of Na+ and B3+ in the DSW always exceeded the maximum thresholds for irrigation water proposed in the literature for citrus, and the concentration of Na+ in the leaves exceeded the maximum threshold in summer 2018. Nonetheless, symptoms of toxicity were not observed. Significant differences among treatments were not observed for Ψstem, A, gs, Na+, Cl−, and B3+ in leaves (except in the summer months), yield components, fruit quality, or the economic assessment. The lack of such differences was explained by the large standard deviations caused by the youth of the trees, with figures that on occasion could represent more than 100% of the mean value. These results may justify the agronomic and economic viability of the irrigation of young trees with DSW in the short-term, but further research, considering the effects on adult trees in the long term is still needed.