We study nonsequential triple ionization of Ar in strong laser fields using a classical trajectory Monte Carlo simulation. By tracing electrons' trajectories, we reveal the mechanisms of triple ionization, including multiple recollision and sequential ionization. One electron tunnels out and rescatters with its parent ion, either kicking off two electrons together or kicking off one of them and exciting another one, which will be freed by the laser field. Besides the above-dominated channels, the cascade rescattering for triple ionization is explored, in which the first tunneling electron rescatters with the parent ion ${\mathrm{Ar}}^{+}$ and kicks off the second electron and then the second electron gains energy in the laser field and rescatters with ${\mathrm{Ar}}^{2+}$, kicking off the third electron or boosting it to excited states to be freed later. Such a cascade channel connects three electrons step by step, and ${\mathrm{Ar}}^{3+}$ may have larger ultimate momenta compared to the triple ionization mediated by only one rescattering. Our simulation shows it is possible to control the cascade channel and extract it through the ion momentum distribution.