We report upon the specific heat and magnetocaloric properties of Cu2MnBO5 over a temperature range of 60-350 K and in magnetic fields up to 18 kOe. It is found that at temperatures below the Curie temperature (TC ∼ 92 K), CP(T)/T possesses a linear temperature-dependent behavior, which is associated with the predominance of two-dimensional antiferromagnetic interactions of magnons. The temperature independence of CP/T = f(T) is observed in the temperature range of 95-160 K, which can be attributed to the excitation of the Wigner glass phase. The magnetocaloric effect [i.e., the adiabatic temperature change, ΔTad (T,H)] is assessed through a direct measurement or an indirect method using the CP(T,H) data. Owing to its strong magnetocrystalline anisotropy, an anisotropic magnetocaloric effect (MCE) or the rotating MCE [ΔTadrot (T)] is observed in Cu2MnBO5. A deep minimum in the ΔTadrot (T) near the TC is observed and ascribed to the anisotropy of the paramagnetic susceptibility.