This paper deals with one of the methods asteroid hazard mitigation. The preventive destruction of a hazardous asteroid during the previous close encounter before its predicted collision is considered. Two variants of the explosion are considered: In the first case a projectile overtakes an asteroid; in the second one the situation is contrary. The second way requires significantly lower velocity of spacecraft delivery. On the other hand, it loses to the first way, since the number of fragments falling to the Earth is about an order of magnitude larger. However, with a more careful approach (non-isotropic explosion), this unfavorable factor can be likely reduced.