We present the results of classical molecular dynamics simulations of collision-induced fusion and fragmentation of C60 fullerenes, performed by means of the MBN Explorer software package. The simulations provide information on structural differences of the fused compound depending on kinematics of the collision process. The analysis of fragmentation dynamics at different initial conditions shows that the size distributions of produced molecular fragments are peaked for dimers, which is in agreement with a well-established mechanism of C60 fragmentation via preferential C2 emission. Atomic trajectories of the colliding particles are analyzed and different fragmentation patterns are observed and discussed. On the basis of the performed simulations, characteristic time of C2 emission is estimated as a function of collision energy. The results are compared with experimental time-of-flight distributions of molecular fragments and with earlier theoretical studies. Considering the widely explored case study of C60-C60 collisions, we demonstrate broad capabilities of the MBN Explorer software, which can be utilized for studying collisions of a broad variety of nanoscale and biomolecular systems by means of classical molecular dynamics.