The entropy and cooling property of the mixed spin-(1/2, 1) Ising-Heisenberg double saw-tooth ladder are rigorously examined under an adiabatic demagnetization process using the classical transfer-matrix formalism. The model is characterized once by XXX and once by XX interactions between the interstitial Heisenberg dimers. An Ising-type coupling links spins localized on the legs and rungs. We investigate the ability of cooling/heating of the models nearby some typical critical points. It is evidenced that both models exhibit an enhanced magnetocaloric effect in a proximity of the magnetization steps and jumps. During an adiabatic demagnetization process, a sharp temperature drop is seen close to the first-order zero-temperature phase transitions. We conclude that the single-ion anisotropy considered for the integer spins plays an essential role to determine an efficiency of the magnetocaloric effect of the models under consideration.