The use of bacteriophages for killing pathogenic bacteria is a feasible alternative to antibiotics and disinfectants. To obtain the large quantities of phages required for this application, large-scale production of bacteriophages must be optimized. This study aims to define conditions that maximize the phage yield of the virulent and polyvalent staphylococcal bacteriophage vB_SauM-phiIPLA-RODI in broth culture, using the food-grade species Staphylococcus xylosus as the host strain to reduce the risk of growing massive quantities of pathogenic bacteria and therefore, to ensure the safety of the final phage stock. The effect of four variables, namely initial bacterial concentration (5.66–8.40 log10 colony-forming unit (CFU)/mL), initial phage concentration (5–8 log10 plaque-forming unit (PFU)/mL), temperature (21–40 °C) and agitation (20–250 rpm), on phage yield (response) was studied by using response surface methodology (RSM). Successive experimental designs showed that agitation did not significantly impact phage yield, while temperature did have a significant effect, with 38 °C being the optimum for phage propagation. The results allowed the design of a model to describe phage yield as a function of the initial bacterial and phage concentrations at fixed agitation (135 rpm), and optimum temperature (38 °C). The maximum experimental phage yield obtained was 9.3 log10 PFU/mL, while that predicted by the model under the optimized conditions (7.07 log10 CFU/mL initial bacterial population and 6.00 log10 PFU/mL initial phage titer) was 9.25 ± 0.30 log10 PFU/mL, with the desirability of 0.96. This yield is comparable to that obtained when the phage was propagated on the original host, Staphylococcus aureus. Bacteriophage phiIPLA-RODI showed the same host range and very similar biofilm removal ability regardless of the staphylococcal species used for its propagation. The results presented in this study show the suitability of using a food-grade strain of S. xylosus for the propagation of S. aureus infecting phages and the application of RSM to define the optimal propagation conditions.