Magnesium (Mg) alloys have attracted great attention as potential materials for biodegradable implants. It is essential that an implant material possesses adequate resistance to cracking/fracture under the simultaneous actions of corrosion and mechanical stresses, i.e., stress corrosion cracking (SCC) and/or corrosion fatigue (CF). This study investigates the deformation behaviour of a newly developed high-strength low-alloy Mg alloy, MgZn1Ca0.3 (ZX10), processed at two different extrusion temperatures of 325 and 400 °C (named E325 and E400, respectively), under slow strain tensile and cyclic tension-compression loadings in air and modified simulated body fluid (m-SBF). Extrusion resulted in a bimodal grain size distribution with recrystallised grain sizes of 1.2 μm ± 0.8 μm and 7 ± 5 μm for E325 and E400, respectively. E325 possessed superior tensile and fatigue properties to E400 when tested in air. This is mainly attributed to a grain-boundary strengthening mechanism. However, both E325 and E400 were found to be susceptible to SCC at a strain rate of 3.1×10−7 s−1 in m-SBF. Moreover, both E325 and E400 showed similar fatigue strength when tested in m-SBF. This is explained on the basis of crack initiation from localised corrosion following tests in m-SBF.