One of the lightest metallic materials used in the aeronautics, aerospace, and automotive industries, among others, is magnesium, due to its excellent weight/strength ratio. Most parts used in these industries need to be made of materials that are rigid, strong, and lightweight, but sometimes the materials do not simultaneously satisfy all of the properties required. An alternative is to combine two or more materials, giving rise to a hybrid component that can satisfy a wider range of properties. The pieces machined in these industrial fields must satisfy stringent surface roughness requirements that conform to the design specifications. This work shows an experimental study to analyse the surface roughness reached in hybrid components made up of a base of magnesium alloy (UNS M11917) and two inserts of aluminium alloy (UNS A92024) obtained by turning. Its purpose is to determine the influence of the factors and their possible interactions on the response variable, the surface roughness Ra. The study is carried out using a design of experiments (DOE). A product of a full factorial 23 and a block of two factors 3 × 2 was selected. The factors identified as possible sources of variation of the surface roughness are: depth of cut, feed rate, spindle speed, type of tool, location with respect to the specimen (LRS), and location with respect to the insert (LRI). Data were analysed by means of the analysis of variance (ANOVA) method. The main conclusion is the possibility to carry out the repair and maintenance of parts of magnesium–aluminum hybrid components by dry turning; that is, without cutting fluids and, therefore, in the most sustainable way that the process can be carried out. In addition, different combinations of cutting parameters have been identified that allow these operations to be carried out in an efficient manner, reducing mechanization times and, therefore, also the direct and indirect costs associated with them.