A high strength-to-mass ratio makes the use of metal matrix composites acceptable for a wide range of engineering applications. However, their use is often complicated, and machining such composites involves several challenges. During the machining process, controllable machining parameters need to be optimised to achieve multiple objectives. In this work, an attempt was made to streamline the turning parameters of a magnesium/alumina hybrid composite under dry and minimum quantity lubrication (MQL) cutting conditions. Experiments were carried out based on Taguchi's L18 orthogonal array. The input parameters (i.e. cutting conditions, cutting speed, feed and depth of the cut) were considered the cutting factors, while surface roughness, cutting force, specific power consumption, and cutting temperature were the response variables. A grey relational analysis (GRA) and the techniques for order preferences by similarity to ideal solution (TOPSIS) method were employed to improve the straight turning process of hybrid composites and to optimise the input control factors. The percentage contribution of each input parameter was identified by creating an analysis of variance (ANOVA) table. Based on the data given in the response table and the ANOVA table for the GRA and TOPSIS, feed rate was found to be the most influential parameter of those investigated in the present study, followed by the depth of cut, cutting conditions, and cutting speed. The GRA and TOPSIS produced two unique sets of optimised parameters. The optimised parameter combinations obtained using the GRA method were cutting condition = MQL, cutting speed = 100 m/min, feed rate = 0.15 mm/rev, and depth of cut = 0.50 mm; using the TOPSIS, the optimal value for cutting speed changed to 150 m/min when all other parameter values were kept the same as they were for the GRA. However, from the results of the validation tests, it was clear that the optimised parameters obtained from the TOPSIS produced a machined composite with better properties than the composite produced using the GRA.