Dimethyl ether is a new-generation alternative fuel to mitigate cold-start issues in compression ignition engines. It has a higher cetane number and offers superior spray atomization and fuel evaporation characteristics. This simulation study compares dimethyl ether and baseline diesel sprays and their evaporation characteristics in a constant volume spray chamber. Fuel properties greatly influence spray atomization and evaporation characteristics. This study is based on the Eulerian–Lagrangian approach adopted in the Reynolds-averaged Navier–Stokes framework. The liquid spray penetration obtained by simulation matched well with the experimental results of dimethyl ether and baseline diesel. Spray model constants were tuned for diesel and dimethyl ether separately, as the fuel properties of both test fuels are completely different. These tuned models were used to simulate dimethyl ether and diesel sprays at fixed fuel injection timings and ambient conditions. Results showed a lower spray penetration length for dimethyl ether than baseline diesel because of the flash boiling of dimethyl ether. Smaller diameter droplets formed due to dimethyl ether’s lower viscosity, density, surface tension, and higher evaporation rate. The reduction in Sauter mean diameter was quite sharp after the start of injection for the dimethyl ether. Diesel spray showed retarded spray atomization and evaporation characteristics compared to dimethyl ether. The vapor penetration length of both fuels was almost the same; however, the vapor mass fraction was higher for dimethyl ether than baseline diesel. Dimethyl ether spray exhibited superior spray atomization and improved evaporation of fuel droplets.