We study the explosion dynamics of rare-gas clusters $({\mathrm{Ar}}_{55}, {\mathrm{Ar}}_{147}, {\mathrm{Xe}}_{55},$ and ${\mathrm{Xe}}_{147})$ in an intense, femtosecond laser pulse via Monte Carlo classical particle-dynamics simulations. Our method includes tunnel and impact ionization as well as ion-electron recombination, and allows us to follow the motion of both ions and free electrons during laser-cluster interaction. Our simulation results show that ionization proceeds mainly through tunnel ionization by the combined fields from ions, electrons, and laser while the contribution of electron-impact ionization is secondary. The ions are ejected in a stepwise manner from outer shells and accelerated mainly through their mutual Coulomb repulsion. Taking a spatial laser intensity profile into account, we show that the Coulomb explosion scenario leads to the same charge dependence of ion energy, i.e., quadratic for lower charge states and linear for higher ones, as that observed in experiments with larger clusters. This indicates that Coulomb explosion may be a dominant cluster explosion mechanism even in the case of large clusters. We also find that the ion energy is higher in the direction parallel to laser polarization than in the direction perpendicular to it. When ions are emitted along the direction of laser polarization, their charge changes in phase with the laser field, and this leads to an efficient acceleration.