The research was aimed at assessing the effect of the redispersible polymer powder on the fracture resistance of a subbase made of a mineral–cement mixture with a bitumen emulsion. The test was performed at two temperatures, i.e., 0 °C and 20 °C. The prepared mixtures differed in the content of cement, asphalt emulsion, and polymer modifier. Cement and redispersible polymer powder were dosed in 1.5% steps from 0.5% to 3.5% while the amount of bitumen emulsion ranged from 0.0% to 5.0%. The SCB (semi-circular bending) tests carried out in the laboratory showed the dependence of the influence of the amount of binder and polymer modifier on the fracture resistance of the recycled subbase. Mixes containing a polymer modifier in their composition are characterized by a much higher resistance to cracking than traditional mineral–cement–emulsion mixtures. An example is the doubling of the framework’s fracture toughness (KIC) when the amount of the polymer modifier is increased from 0.5% to 2.0% with a constant cement content of 0.5%. The obtained results (KIC) in this case were 2.90 and 5.81. The key is the right ratio of polymer powder and cement in the base composition.