Understanding the water use of drought-tolerant crops of the drought-prone Mediterranean regions is important for sustainable agriculture. The aim of this study was to evaluate the yield and yield responses of amaranth (Amaranthus hybridus L.) to different irrigation strategies conducted in 2019 and 2020 under Mediterranean climatic conditions using surface drip (SD) and subsurface drip (SSD) systems. Strategies investigated were: regulated deficit irrigation (RDI), conventional deficit irrigation (DI25, DI50, DI75), full irrigation (FI) and rainfed treatment. The highest grain yield was observed in FI treatments; RDI treatments produced 5% lower grain yield than the FI treatments, although the RDI treatments resulted in water savings of 23 and 21% for SD and SSD systems, respectively. DI treatments resulted in lower leaf water potential (LWP) and higher crop water-stress index (CWSI) compared to FI in both systems values. The results showed that optimum irrigation conditions to obtain the highest amaranth grain yields were associated with an LWP of −1.0 MPa and an average CWSI of about 0.25. The FI treatments under SSD systems had the highest grain production, followed by FI under SD and RDI under both the drip systems. Under SD and SSD systems, RDI saved 23 and 21% water, respectively, and produced a yield statistically comparable to that of FI. The SSD methods generated higher net income than SD. From these results it can be concluded that both RDI and DI75 could be a good alternative to FI under the conditions of water scarcity in the Mediterranean region.