To establish the fundamental understanding of the fragmentation dynamics of highly positive charged nano- and bio-materials, we carried out on-the-fly classical trajectory calculations on the fragmentation dynamics of C60(q+) (q = 20-60). We used the UB3LYP/3-21G level of density functional theory and the self-consistent charge density-functional based tight-binding theory. For q ≥ 20, we found that a two-step explosion mechanism governs the fragmentation dynamics: C60(q+) first ejects singly and multiply charged fast atomic cations C(z+) (z ≥ 1) via Coulomb explosions on a timescale of 10 fs to stabilize the remaining core cluster. Thermal evaporations of slow atomic and molecular fragments from the core cluster subsequently occur on a timescale of 100 fs to 1 ps. Increasing the charge q makes the fragments smaller. This two-step mechanism governs the fragmentation dynamics in the most likely case that the initial kinetic energy accumulated upon ionization to C60(q+) by ion impact or X-ray free electron laser is larger than 100 eV.